<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-08-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001140859</issuerCik>
        <issuerName>Cencora, Inc.</issuerName>
        <issuerTradingSymbol>COR</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001882641</rptOwnerCik>
            <rptOwnerName>Campbell Elizabeth S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>1 WEST FIRST AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CONSHOHOCKEN</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19428</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive Vice President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-08-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>11300.471</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>324.116</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19455.085</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The sale price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions ranging from $324.06 to $324.37 inclusive. The reporting person undertakes to provide to the Company, any security holder of the Company or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each price within the ranges set forth in this footnote.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Elizabeth S. Campbell</signatureName>
        <signatureDate>2026-08-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
