Out of sheer curiosity, I've did a quick Google search and it seems that it does not.

https://www.dps.texas.gov/rsd/ltc/faqs/index.htm

> 12. Can non-US citizens obtain a License to Carry a Handgun? > Yes. Subject to the requirements of federal firearms law, and if not otherwise ineligible, resident aliens and certain nonimmigrant aliens who are lawfully present in the United States may obtain the license.