is there a way to find out my rental history for free before applying for an apartment?

Answer 1

your credit report will most likely show some addresses, someone could look up the owners and ask for reference through a city street directory listing

Answer 2

Generally places check your rental history by using the names/numbers YOU Provide on the application. So if you want to check, just call and pretend you are a private renter (like you own a house you're renting out) and want to check to be sure the "applicant' has a good payment history.

Dont try to get crafty and fake the numbers though-- some do verify the #'s are accurate for the complexes using the phone book.