Several counties have already launched their own COVID-19 registration/screening websites to get their residents vaccinated as the state gets more of the Moderna and Pfizer vaccines. Here are some helpful websites.
Dallas County – Register for the COVID-19 Vaccine with DCHHS (if you get an error page, try back again as they update)
Texas Department of State Health Services HERE.
More on the vaccine rollout across Texas here: COVID-19 Vaccine Texas