Armstrong County is a county located in the U.S. state of Texas. As of the 2020 census, the population of Armstrong County was 1,848. It is in the Texas Panhandle and its county seat is Claude. As of the 2020 census, its population was 1,848. Armstrong County is included in the Amarillo metropolitan area. The county was formed in 1876 and later organized in 1890. It was named for one of several Texas pioneer families named Armstrong.