Clifton is a town in Greenlee County, Arizona, United States, on the San Francisco River. According to 2006 Census Bureau estimates, the population of the town is 2,265. The town is the county seat of Greenlee County. It was a site of the Arizona Copper Mine Strike of 1983. Clifton apartments for rent comparison page shows most up to date rent information on Clifton apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.