It is possible, indeed, but only those non citizens who have work permits from DHS or Homeland Security, can apply.
I assume you don't have a DHS work permit but need a SSN?
Yes, i don't have a work permit but i'm in need of a SSN.
Well, being that the case, you'll need to look for more information. you can search under "If you don't have permission to work" section in our printed information.