What does your credit score have to be to rent a house in Arizona? There's no specific credit score requirement in Arizona.In this article, we provide an overview of Arizona rental applications and a free downloadable rental application form. The combined average credit score of all Applicants must be equal or greater than 600. Co-signors will not be accepted. Get Arizona tenant screening background checks now! Apartment tenant screening services include credit, eviction, criminal and more for all of Arizona. Arizona Rental Credit Check - What should be included? Please note, you must reside in the CAP office's service area in order to apply. Contact Us. Have a question?