there is public land open to hunting in that part of the state but its pretty much draw only there like a lot of other western states.
Here's a list of the draw hunts for this year, including aoudad, oryx, axis, gemsbock and waterbuck. I believe the Devils' River unit is one of the one's that hold elk. $3 for the drawing application and $130 for the tag if drawn.
https://www2.tpwd.state.tx.us/huntw...ing/hunt-category-details.phtml?OCat=EXO[edited because left referenced link off the first time]
