From the Texas Parks & Wildlife Department, which is the agency that regulates hunting.

Distribution
Historical evidence indicates that elk may have been present over much of Texas. By the late 1800’s, records indicate that elk were only present in the Guadalupe Mountains of far west Texas. Currently, free ranging elk exist over a large portion of west Texas and on high fence ranches throughout the state.

http://tpwd.texas.gov/huntwild/wild/species/elk/