Briscoe County is a county located in the U.S. state of Texas. As of 2010 census, the population was 1,637. Its county seat is Silverton. The county was created in 1876 and later organized in 1892. It is named for Andrew Briscoe, a soldier during the Texas Revolution.At one time, the large JA Ranch, founded by Charles Goodnight and John George Adair, reached into Briscoe County. After he left the JA, Goodnight owned the Quitaque Ranch.