Roscoe is a city in central Edmunds County, South Dakota, United States. The population was 269 at the 2020 census. Roscoe was laid out in …Roscoe is a city in central Edmunds County, South Dakota, United States. The population was 269 at the 2020 census. Roscoe was laid out in 1877, and named in honor of Roscoe Conkling, a United States Senator from New York.