20 CFR § 422.104 - Who can be assigned a social security number.
(1) A United States citizen; or
(2) An alien lawfully admitted to the United States for permanent residence or under other authority of law permitting you to work in the United States (§ 422.105 describes how we determine if a nonimmigrant alien is permitted to work in the United States); or
(3) An alien who cannot provide evidence of alien status showing lawful admission to the U.S., or an alien with evidence of lawful admission but without authority to work in the U.S., if the evidence described in § 422.107(e) does not exist, but only for a valid nonwork reason. We consider you to have a valid nonwork reason if:
(i) You need a social security number to satisfy a Federal statute or regulation that requires you to have a social security number in order to receive a Federally-funded benefit to which you have otherwise established entitlement and you reside either in or outside the U.S.; or
(ii) You need a social security number to satisfy a State or local law that requires you to have a social security number in order to receive public assistance benefits to which you have otherwise established entitlement, and you are legally in the United States.
(b) Annotation for a nonwork purpose. If we assign you a social security number as an alien for a nonwork purpose, we will indicate in our records that you are not authorized to work. We will also mark your social security card with a legend such as “NOT VALID FOR EMPLOYMENT.” If earnings are reported to us on your number, we will inform the Department of Homeland Security of the reported earnings.