Benson is a city in Cochise County, Arizona, United States. As of the 2010 census, the population of the city was 5,105. It was founded as a rail …Benson is a city in Cochise County, Arizona, United States. As of the 2010 census, the population of the city was 5,105. It was founded as a rail terminal for the area, and located approximately 45 miles east-southeast of the city of Tucson.