You can only apply for a Social Security number if you have permission to work from the DHS.
Are you a noncitizen with permission to work in the U.S,?
Yes, I have permission to work.
Unfortunately, no relevant information is found.
What if I'm a J-1 student?
In this case, you will need to provide us a letter from your sponsor. This letter should be on sponsor letterhead with an original signature that authorizes your employment.
I still need to ask another question about being a noncitizen with permission to work in the U.S.  How do I prove the status of my immigration?
You must show current immigration documents such as Form l-551 lawful permanent resident card or employment authorization document, work permit
Are you a F-1 or M-1 student?
How do I prove F-1 or M-1 student eligiblility
your must show us your 1-20 certificate of eligiblity for nonimmigrant studen status
Can I get services without a social security number
you can get many benifits and services without a social security nuber such as to conduct business with a bank, register for school , private health insurance , educational test, apply for school lunch programs of apply for subsidized housing
Where would a bring my documents?