Arizona is a largely arid state with relatively limited wild trout habitat. However, wherever the elevation climbs around 5,000 feet or higher, there's a shot at cold water habitat that can support wild trout. Arizona supports its own native trout: the Apache, and also supports a few streams with Gila Trout (which are predominantly found in NM).
Note that a significant amount of trout habitat is found on Indian reservations, where fishing is regulated by each tribe. You do not need an AZ license to fish on a reservation, but you will need a tribal permit, and many areas are closed to angling. Generally speaking Apache Trout not found on Indian reservations can be legally caught. Gila trout streams are all closed to fishing, even those not found on reservations.