What are ways to get approved with no rental history? Yes you can fill out without having prior rental history.Yes, you can rent an apartment with no rental history. But you're going to have to provide the paperwork that proves you can afford it. List Reputable References. Although applications can typically be processed within 2-3 days, circumstances may result in processing that may take up to one week to complete. A landlord may ask you to fill out a rental application. Rental history reports help paint a picture of a tenant's past behavior. A landlord may ask you to fill out a rental application. Please note: Application fee is non-refundable.