TMZ reported that the driver, who it said was working for Uber, claims he was slapped in the head by the "Silicon Valley" star when they arrived at his home.
It was not immediately clear which side of the Trump row Miller was on, but he has been an outspoken critic of the real estate mogul in the past.
Officers arrested Miller at a private address around 1:00 am (0900 GMT) and took him into custody, LAPD officer Jenny Hauser said.
The actor, who was charged with battery, posted $20,000 bail. He was released just under five hours later and ordered to appear in court on January 9.
Hauser would not confirm that the driver worked for Uber, adding: "All I can say is that he was a driver for a transportation company."
Miller's disdain for Trump was on display on Election Day on November 8 when he tweeted: "Please prevent @realDonaldTrump from putting his name on the White House in cheap gold."
When Miller appeared on TBS show "Conan" a few days prior, the actor set fire to a Trump tie he said he had bought "back when Donald Trump was funny."