It's important to note that landlords are unable to check a tenant's credit history without a social security number, since there is no way to pull information from any of the credit bureaus.
Some states, such as California, prohibit a landlord from inquiring about a tenant's or prospective tenant's immigration status or citizenship and requiring proof of legal residency or citizenship as a prerequisite to renting.
Before you move in, you'll need to prepare all of your necessary documents. This includes your driver's license or ID, Social Security Number, birth certificate, and more. You'll also need to provide proof of income and previous rental history.
Rental, credit and employment information is generally referenced and submitted in form of a letter or sometimes by a phone call. Renters need to have a social security number. If you do not have a social security number or are not applying for one you must have a guarantor co-signing your lease.
Although not all landlords will need you to have a Social Security number, pretty much all of them will require some sort of legal documentation, so be sure to have that ready before you start apartment hunting.