Under Texas law, the authority to grant pardons and clemency is vested in the governor. See: http://www.tdcj.state.tx.us/bpp/exec_clem/exec_clem.html.
You should consult with a Texas lawyer in order to evaluate options you may have to minimize or eliminate the adverse consequences flowing from your conviction.
The only one who can grant a pardon is the Governor of the state. However, if its a federal crime, which it doesn't sound like, then it would take a Presidential pardon to have it removed.
You may have a right to sealing and/or expungement and that could be granted by a local judge.
Consult with a local attorney to see if you meet the conditions for sealing your record.
Depending on how the charge was resolved- if a deferred adjudication- you might be entitled to seal the record. If not, and it's a conviction your only hope is a pardon by the governor of the state.