Rent A Center does not check your credit score but they will need you to provide them some phone numbers to at least 5 people that they can call as references to you.
So if you don't have people that can vouch for you or that you can give their number to Rent A Center so they can call those people especially if you miss a payment.
So if you rent from Rent A Center be prepared for them to call up your references on the numbers you give them before you leave the store.