The heavy corrosion tells us two things about your iron buckle's age. (1) It is quite old. That extreme degree of rust-corrosion didn't happen in just a couple of decades... unless it was found in seacoastal salty soil, which yours wasn't. (2) The deep corrosion reveals that the metal it is made of is simple wrought-iron, not 20th-Century steel. So, combining 1 & 2, and its size in your hand, with my presumption that you found it in Arizona, I'd say your buckle (missing its simple iron tongue) is from either the 1800s or early 1900s.
My thought as to what it was used for... the majority of that type of simple wrought-iron buckle were made for use on horse harness ("horse tack").