That depends on whether it’s a misdemeanor or a felony. First and Second Offense DWIs in Texas are Class B, and Class A Misdemeanors, respectively. Third Offense DWI (and above) are Felonies.

Chapter 12 of the Texas Code of Criminal Procedure covers all of the limitations periods for prosecution in Texas. 

All misdemeanors in Texas have a 2 year statute of limitations, including DWI. Felony DWIs fall under the “regular” 3 year statute of limitations.