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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-09-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000096021</issuerCik>
        <issuerName>SYSCO CORP</issuerName>
        <issuerTradingSymbol>SYY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001189793</rptOwnerCik>
            <rptOwnerName>GLASSCOCK LARRY C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1390 ENCLAVE PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77077</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-09-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>285</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>61.17</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>69148.32</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares to be received in lieu of a portion of non-employee director annual cash retainer fees pursuant to the Sysco Corporation 2018 Omnibus Plan, including 204 shares to be received in lieu of the base retainer.  The receipt of these shares has been deferred pursuant to the 2009 Board of Directors Stock Deferral Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gerald W. Clanton, Attorney-in-fact</signatureName>
        <signatureDate>2020-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2020-09-30
0
0000096021
SYSCO CORP
SYY
0001189793
GLASSCOCK LARRY C
1390 ENCLAVE PARKWAY
HOUSTON
TX
77077
1
0
0
0
Common Stock
2020-09-30
4
A
0
285
61.17
A
69148.32
D
Represents shares to be received in lieu of a portion of non-employee director annual cash retainer fees pursuant to the Sysco Corporation 2018 Omnibus Plan, including 204 shares to be received in lieu of the base retainer.  The receipt of these shares has been deferred pursuant to the 2009 Board of Directors Stock Deferral Plan.
/s/ Gerald W. Clanton, Attorney-in-fact
2020-10-01