Ryan Guillen, a democrat from House District 31, filed a bill Monday that would require the Longhorns and Aggies to play each year.
The schools played annually since 1915 until last season, when the series ended when Texas A&M left Texas and the Big 12 for the SEC last season.
"This game is as much a Texas tradition as cowboy boots and barbecue," Guillen said in a statement provided to ESPN. "The purpose of this bill is to put the 'eyes of Texas upon' our two greatest state universities to restore this sacred Texas tradition.
"I think the people of Texas want a game, and we're trying to get them one."
The first meeting between Texas and Texas A&M was in 1894.
Guillen tweeted Monday night that he had filed House Bill 788 requiring the schools to play an annual nonconference, regular-season game.
"We remain hopeful that the game may continue one day through the normal scheduling process," Texas A&M president Dr. R. Bowen Loftin said. "Having said that, we, of course, will follow any specific direction from the Legislature."
A University of Texas spokesman had no comment Monday night.
Guillen is a Texas A&M graduate and represents Rio Grande Valley in south Texas.
Texas won the last meeting against Texas A&M 27-25 on Nov. 24, 2011. The Longhorns lead the series, 76-37-5.