I did a quick google search, and found out that they do indeed offer over the counter licenses for elk in Arizona. I was actually surprised about it. Apparantly, they are for a VERY limited number of areas, and there is mostly private land and very low elk numbers in these units.
I could not find any reference to if it was open to non-residents. It doesn't say either way. Here is a link to the website so you can read for yourself.
Want a quick and inexpensive call for Moose? Take an empty 32 ounce coffee can, and make a small slit in the bottom, only about a quarter inch. Then, take one of those really big red rubber bands, the ones that go around big folders. Cut the rubber band to make one long piece.
Now, thread one end of the band and tie a knot on the outside of the can so it won't pull through. Cut the band off on the other side so it is even with the top of the can.
Now, wet your finger,...