Azle is a city west of Fort Worth in Parker and Tarrant Counties in the U.S. state of Texas. As of the 2020 census, the city population was 13,36…Azle is a city west of Fort Worth in Parker and Tarrant Counties in the U.S. state of Texas. As of the 2020 census, the city population was 13,369. Azle is the home of the Azle Marching Green Pride marching band and the Fighting Azle Hornets.