Most apartment buildings don't rent to young people with no rental history or at least those are all the ones that I've seen so far. What are ways to get approved with no rental history?List Reputable References. 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. Many standard forms are available below. All forms are categorized into their respective departments. Applicants with no rental history could ask their boss or manager for a personal reference letter. It is possible to submit an application without having rented in the past. On the Residence History step, enter your current address, and set dates.