If you are the nonresident spouse of a nonresident service member stationed in Arizona, the income you earn in Arizona is not taxed by Arizona. That income is instead taxable by the state you and the service member call home.
There is nothing to apply for with Arizona. Give your Arizona employer your out-of-state residency information so Arizona tax is not withheld, and report the income on your home state return.
The service member’s military orders assigning them to Arizona, and proof that you and the service member are residents of another state, such as a driver license or voter registration.