Riverton is a city in Fremont County, Wyoming, United States. The city's population was 10,682 at the 2020 census, making it the most populo…Riverton is a city in Fremont County, Wyoming, United States. The city's population was 10,682 at the 2020 census, making it the most populous city in the county. The city, founded in 1906, is an incorporated entity of the state of Wyoming. The community was named Riverton because of the four rivers that meet there. The town was built on land ceded from the Wind River Indian Reservation, a situation that often makes it subject to jurisdictional claims by the nearby Eastern Shoshone and Northern Arapaho tribes.