According to the IRS:
To claim the EITC, you and your spouse (if filing jointly) must be U.S. citizens or resident aliens.
If you or your spouse were a nonresident alien for any part of the tax year, you can only claim the EITC if your filing status is married filing jointly and you or your spouse is a:
U.S. Citizen with a valid Social Security number or
Resident alien who was in the U.S. at least 6 months of the year you’re filing for and has a valid Social Security number
Please go through this IRS interview to see if you are eligible
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