Gov. Rick Perry has not said if he would sign the legislation, the Austin American-Statesman reported. A number of cities in the state, including Austin, already have texting bans.
"I think it's a good law enforcement tool to keep streets and roads safe for every Texan," said Rep. Tom Craddick, a Republican who sponsored the bill. "It'll make our roads as safe as possible."
The ban would also apply to instant messaging behind the wheel. There are exceptions for drivers in emergency situations.
Drivers who violate the law would face penalties of up to 30 days in jail or fines of up to $200. Penalties would be heavier if the texting causes a crash.
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph
Exploding whale video goes viral on Internet