My spouse lives in another country and is a NRA . Should I file a joint return even if she doesn’t have a social security number? Can I get the earn income credit

If your spouse does not have a social security number, you will not be able to claim the earned income credit.

If you are not applying for an ITIN (Individual Taxpayer Identification Number) for your spouse with your return, you will not be able to file married filing jointly.  An ITIN is not a SSN.  It is a number that is used for tax purposes and is applied for when someone does not qualify for a SSN.   You would need to complete a W-7 and provide the appropriate documentation with your jointly filed return.  Please see the links below:

Form W-7     Instructions for Form W-7

Your other choice is to file married filing separately.