Mark Nothaft answers the question Was the Civil War fought in Arizona? No, but yes. The westernmost battle of the civil war took place in what is now the state of Arizona, but it was part of the New Mexico Territory when the actual battle took place.
Today, you can watch reenactments, visit memorials and learn more about the battle at the interpretive center on a 3,750 acre park. This article contains a link to the information you need about the reenactment and contains many more details about the battle.