<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019d69de-be32-7a9f-816c-0b6d743a9139,g:edd3cc8c-51dd-40d6-802c-fc2f5de9ffe6-->
<link:linkbase 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" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://xbrl.sec.gov/ecd/role/AwardTimingDisclosure" xlink:type="simple" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#AwardTimingDisclosure"/>
  <link:presentationLink xlink:role="http://xbrl.sec.gov/ecd/role/AwardTimingDisclosure" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:loc xlink:type="locator" xlink:label="loc_rnac_CarstenBrunnPh.D.Member" xlink:href="rnac-20260428.xsd#rnac_CarstenBrunnPh.D.Member"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="loc_rnac_CarstenBrunnPh.D.Member" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_rnac_BlaineDavisMember" xlink:href="rnac-20260428.xsd#rnac_BlaineDavisMember"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="loc_rnac_BlaineDavisMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_rnac_ChristopherJewellPh.D.Member" xlink:href="rnac-20260428.xsd#rnac_ChristopherJewellPh.D.Member"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="loc_rnac_ChristopherJewellPh.D.Member" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_rnac_MetinKurtogluM.D.Ph.D.Member" xlink:href="rnac-20260428.xsd#rnac_MetinKurtogluM.D.Ph.D.Member"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="loc_rnac_MetinKurtogluM.D.Ph.D.Member" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
  </link:presentationLink>
</link:linkbase>