<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Linkbase Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2022-08-15T01:11:25.1983+00:00 -->
<!-- Copyright (c) 2022 Donnelly Financial Solutions, Inc. All Rights Reserved. -->
<link:linkbase xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <link:roleRef roleURI="http://alaunos.com/20220630/taxonomy/role/BalanceSheets" xlink:href="tcrt-20220630.xsd#BalanceSheets" xlink:type="simple"/>
  <link:roleRef roleURI="http://alaunos.com/20220630/taxonomy/role/DisclosureDebtScheduleOfDebtDetails2" xlink:href="tcrt-20220630.xsd#DisclosureDebtScheduleOfDebtDetails2" xlink:type="simple"/>
  <link:roleRef roleURI="http://alaunos.com/20220630/taxonomy/role/DisclosureLeasesOperatingLeaseLiabilitiesDetails2" xlink:href="tcrt-20220630.xsd#DisclosureLeasesOperatingLeaseLiabilitiesDetails2" xlink:type="simple"/>
  <link:roleRef roleURI="http://alaunos.com/20220630/taxonomy/role/StatementsOfOperations" xlink:href="tcrt-20220630.xsd#StatementsOfOperations" xlink:type="simple"/>
  <link:roleRef roleURI="http://alaunos.com/20220630/taxonomy/role/StatementsOfCashFlows" xlink:href="tcrt-20220630.xsd#StatementsOfCashFlows" xlink:type="simple"/>
  <link:roleRef roleURI="http://alaunos.com/20220630/taxonomy/role/DisclosureLeasesOperatingLeaseLiabilitiesDetails" xlink:href="tcrt-20220630.xsd#DisclosureLeasesOperatingLeaseLiabilitiesDetails" xlink:type="simple"/>
  <link:calculationLink xlink:type="extended" xlink:role="http://alaunos.com/20220630/taxonomy/role/BalanceSheets">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_Liabilities" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_AssetsCurrent" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_AccountsPayableCurrent" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_LiabilitiesCurrent" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_CommonStockValue" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_CommitmentsAndContingencies" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LongTermDebtCurrent" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_ReceivablesNetCurrent" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_AdditionalPaidInCapitalCommonStock" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_LongTermDebtNoncurrent" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_PropertyPlantAndEquipmentNet" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_StockholdersEquity" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_AccruedLiabilitiesCurrent" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_PrepaidExpenseAndOtherAssetsCurrent" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_OtherLiabilitiesNoncurrent" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_DepositsAssetsNoncurrent" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OtherAssetsNoncurrent" order="4" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LongTermDebtCurrent" xlink:label="us-gaap_LongTermDebtCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ReceivablesNetCurrent" xlink:label="us-gaap_ReceivablesNetCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AdditionalPaidInCapitalCommonStock" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LongTermDebtNoncurrent" xlink:label="us-gaap_LongTermDebtNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccruedLiabilitiesCurrent" xlink:label="us-gaap_AccruedLiabilitiesCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherLiabilitiesNoncurrent" xlink:label="us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DepositsAssetsNoncurrent" xlink:label="us-gaap_DepositsAssetsNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FinanceLeaseLiabilityCurrent" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherAssetsNoncurrent" xlink:label="us-gaap_OtherAssetsNoncurrent"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://alaunos.com/20220630/taxonomy/role/DisclosureDebtScheduleOfDebtDetails2">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_DebtInstrumentCarryingAmount" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_LongTermDebtCurrent" order="1" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LongTermDebtNoncurrent" xlink:label="us-gaap_LongTermDebtNoncurrent"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DebtInstrumentCarryingAmount" xlink:label="us-gaap_DebtInstrumentCarryingAmount"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LongTermDebtCurrent" xlink:label="us-gaap_LongTermDebtCurrent"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://alaunos.com/20220630/taxonomy/role/DisclosureLeasesOperatingLeaseLiabilitiesDetails2">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_OperatingLeaseLiability" order="1" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingLeaseLiability" xlink:label="us-gaap_OperatingLeaseLiability"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://alaunos.com/20220630/taxonomy/role/StatementsOfOperations">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_ResearchAndDevelopmentExpense" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingExpenses" order="0" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_InterestExpense" order="1" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_GeneralAndAdministrativeExpense" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NonoperatingIncomeExpense" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="tcrt_GainLossOnOperatingLeaseModification" order="2" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss" order="4" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingExpenses" xlink:label="us-gaap_OperatingExpenses"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ResearchAndDevelopmentExpense" xlink:label="us-gaap_ResearchAndDevelopmentExpense"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InterestExpense" xlink:label="us-gaap_InterestExpense"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense"/>
    <link:loc xlink:type="locator" xlink:href="tcrt-20220630.xsd#tcrt_GainLossOnOperatingLeaseModification" xlink:label="tcrt_GainLossOnOperatingLeaseModification"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://alaunos.com/20220630/taxonomy/role/StatementsOfCashFlows">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromIssuanceOfLongTermDebt" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetIncomeLoss" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" order="0" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_Depreciation" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_PaymentsOfDebtIssuanceCosts" order="1" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromStockOptionsExercised" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AmortizationOfFinancingCosts" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_SaleOfStockConsiderationReceivedOnTransaction" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_GainLossOnTerminationOfLease" order="4" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="tcrt_NetProceedsFromAtTheMarketStockOffering" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInReceivables" order="5" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" order="6" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="tcrt_IncreaseDecreaseInRightOfUseAsset" order="7" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" order="8" weight="-1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable" order="9" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilities" order="10" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="tcrt_IncreaseDecreaseInLeaseLiabilities" order="11" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" order="12" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_Depreciation" xlink:label="us-gaap_Depreciation"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PaymentsOfDebtIssuanceCosts" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromStockOptionsExercised" xlink:label="us-gaap_ProceedsFromStockOptionsExercised"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AmortizationOfFinancingCosts" xlink:label="us-gaap_AmortizationOfFinancingCosts"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_GainLossOnTerminationOfLease" xlink:label="us-gaap_GainLossOnTerminationOfLease"/>
    <link:loc xlink:type="locator" xlink:href="tcrt-20220630.xsd#tcrt_NetProceedsFromAtTheMarketStockOffering" xlink:label="tcrt_NetProceedsFromAtTheMarketStockOffering"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInReceivables" xlink:label="us-gaap_IncreaseDecreaseInReceivables"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:loc xlink:type="locator" xlink:href="tcrt-20220630.xsd#tcrt_IncreaseDecreaseInRightOfUseAsset" xlink:label="tcrt_IncreaseDecreaseInRightOfUseAsset"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInAccountsPayable" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <link:loc xlink:type="locator" xlink:href="tcrt-20220630.xsd#tcrt_IncreaseDecreaseInLeaseLiabilities" xlink:label="tcrt_IncreaseDecreaseInLeaseLiabilities"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities"/>
  </link:calculationLink>
  <link:calculationLink xlink:type="extended" xlink:role="http://alaunos.com/20220630/taxonomy/role/DisclosureLeasesOperatingLeaseLiabilitiesDetails">
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" order="0" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" order="1" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" order="2" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" order="3" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" order="4" weight="1" use="optional"/>
    <link:calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="tcrt_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" order="5" weight="1" use="optional"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:loc xlink:type="locator" xlink:href="tcrt-20220630.xsd#tcrt_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:label="tcrt_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour"/>
  </link:calculationLink>
</link:linkbase>
