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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-08-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000084748</issuerCik>
        <issuerName>ROGERS CORP</issuerName>
        <issuerTradingSymbol>ROG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001463733</rptOwnerCik>
            <rptOwnerName>Pelletier Ronald J.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ROGERS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>ONE TECHNOLOGY DRIVE PO BOX 188</rptOwnerStreet2>
            <rptOwnerCity>ROGERS</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06263-0188</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Corp Controller &amp; PrinAcct Off</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Capital (Common) Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2013-08-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7322.0000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents the award of Time-Based Restricted Stock Units that convert to common stock on a one-for-one basis pursuant to the 2009 Long-Term Equity Compensation Plan.  This Time-Based Restricted Stock Unit award vests in full on the fourth anniversary of the Grant Date provided that the Grantee is then employed by the Company or an Affiliate.  Restricted Stock Units that are unvested as of the date of the Grantee's employment termination for any reason other than death, disability or retirement shall be forfeited.  Should the Grantee die, become disabled or retire during the vesting period, the total number of Restricted Stock Units will be immediately vested.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Thomas E. Blake as Power of Attorney</signatureName>
        <signatureDate>2013-08-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
