A tenant background checks does not require a social security number. Rental agents need to know that you have a steady job so you can pay your rent, which you can't have without a Social Security number.There are companies who will insure your lease payments, but you will have to provide them your SSN so they can run a credit check on you. Ultimately, it is up to you as the landlord to determine whether or not you want to require a Social Security number on your rental application. Is it legal to ask for the social security number in the rental application? You should be able to rent an apartment without a Social Security number provided you have a student visa or Permanent Resident Card (a.k.a. Once you obtain a Rental Application (and SSN), it's your responsibility to secure it for at least 25 months.