Texas does not provide mug shots accessible to the public for free online. They do, however, post names and crimes committed for all offenders in Texas jails.
The Texas Department of Criminal Justice's website provides a search engine that covers all inmates in Texas jails. Although it does not provide mug shots of the criminals, it does provide you with many details, including name, race, gender, crime committed, criminal history, expected release date, location, date of birth, and whether they are able to accept visitors or not. The only way to get mug shots of criminals in Texas is to run background checks on them.