After an unintelligible response, the officer asks, "Nowhere in particular? Why you say that?"
"You didn't see my name?" Zimmerman replies.
"Nuh-uh," the officer says.
"What a coincidence!" the officer adds. "Are you clear of warrants and stuff?"
"Absolutely sir," Zimmerman says.
"Calm down man, you're good," the officer reassures Zimmerman. "I'm going to go back (to check his license), and why don't you slow down a little bit for me. We'll let you off with a warning."
After an unintelligible response from Zimmerman, the officer says, "Just take it easy. Go ahead and shut your glove compartment. Don't play with your firearm."
After returning Zimmerman's license, the officer says, "All right, sir. Slow down." He wishes Zimmerman a safe trip.
The traffic stop was first reported by TMZ.
Police records do not show how fast Zimmerman was driving, City Manager Brian Brooks said. Police handled Zimmerman as they would have any other motorist in a comparable situation and gave him no special treatment, Brooks said.
The city manager repeatedly declined to identify the officer involved in the traffic stop.
"He obviously didn't expect to pull over George Zimmerman. I don't think he wants the notoriety," Brooks said.
Shawn Vincent, a spokesman for Zimmerman's legal team, said the attorneys had not been able to confirm the account of Zimmerman's road stop independently, but he said he had no reason not to believe the report.
"Anytime his life intersects with anyone now, somehow that's news," Vincent said. "How many people, when they get a warning, become a national headline?"
Vincent would not discuss what Zimmerman was doing in Texas or say anything about Zimmerman's current location, citing safety concerns.
Zimmerman's acquittal on July 13 prompted rallies nationwide calling for a civil rights probe and federal charges against him.
Last year's shooting of Martin, an unarmed black teen, initiated a national dialogue about equal justice, racial profiling, gun control and self-defense laws.
Protesters nationwide lashed out against police in Sanford, Fla., as it took 44 days for Zimmerman to be arrested. Many, including Martin's parents, said Zimmerman had racially profiled the 17-year-old. Zimmerman identifies himself as Hispanic.
The only other time Zimmerman has been seen in public since his acquittal was when he helped rescue four people from an overturned vehicle following a roadway accident in suburban Orlando.
Associated Press writer Michael Schneider contributed to this report from Orlando, Fla.