I was told I needed to fill out a rental application (where ssn is required) before viewing it because he gets several requests a day. Doing a background check without a Social Security number from a rental can often be done.A tenant background checks does not require a social security number. 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. You can see the online application for a rental property license here. You can rent without a social security number. Each background service has its own protocol. The good news is that you do not need an SSN on an apartment rental application to screen a prospective tenant.