F-1 and J-1 students who are working and in legal status can apply for a SSN. More specifically:
The application must be made before your job at NYU ends or your off-campus work authorization expires. If you are not authorized to work off-campus or don’t have a job on-campus, then you are ineligible to apply for a SSN.
Students receiving a fellowship or scholarship who are not expected to work beyond their own studies cannot apply for SSN. Instead, they will be asked by the university to complete, among other papers, a W-7 form to obtain an Individual Taxpayer Identification Number (ITIN) necessary to file their tax forms.
F-2 spouses and family members are NOT eligible to accept employment in the U.S., and are therefore not permitted to apply for Social Security numbers. However, F-2 spouses and family members may apply for Individual Taxpayer Identification Numbers (ITINs) via Form W-7, available through the Internal Revenue Service.
J-2 spouses and family members who have been granted employment authorization by the U.S. Citizenship and Immigration Services may apply for Social Security numbers.
J-2 spouses and family members authorized to work should follow this process to apply:
Note: If you live in New Jersey or elsewhere, please use the Social Security Office Locator to find the center where you should apply.
It’s important that you protect your SSN and guard yourself against identity theft. If you lost your SSN card you will need to reapply for a new one. You can only apply for a replacement card if you are authorized to work off-campus or have an on-campus job at NYU.