Quitaque is a city in southeastern Briscoe County, Texas, United States. The town lies directly south of Caprock Canyon State Park and is a ranching and farming area in West Texas. The population was 411 at the 2010 census.

Briscoe County is a county located in the U.S. state of Texas. As of the 2020 census, the population was 1,435. 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.