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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-02-25</periodOfReport>

    <issuer>
        <issuerCik>0001423689</issuerCik>
        <issuerName>American Capital Agency Corp</issuerName>
        <issuerTradingSymbol>AGNC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001544050</rptOwnerCik>
            <rptOwnerName>Kuehl Christopher</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2 BETHESDA METRO CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>14TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>BETHESDA</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>20814</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior VP</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2015-02-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6145</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.62</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>217328</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>IRA</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Sales made pursuant to a previously established Rule 10b5-1 Plan.</footnote>
        <footnote id="F2">Includes 5,265.679, 1,878.714, 1,888.408 and 1,965.501 shares of stock received pursuant to the reinvestment of cash dividends declared by the Company to holders of record of common stock as of September 30, 2014, October 31, 2014, November 28, 2014 and December 31, 2014, respectively.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Christopher Kuehl</signatureName>
        <signatureDate>2015-02-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
