Rich, 34, who played Nicholas on the series, was booked for investigation of driving under the influence, CHP Officer Francisco Villalobos said.
Rich was driving on Interstate 10 when he almost hit a CHP patrol car parked in a lane that was closed for maintenance, authorities said.
Officers stopped the actor and smelled marijuana inside his vehicle, said CHP Officer John Escobedo. No marijuana was found but Rich was arrested after he failed field sobriety tests, Escobedo said.
Rich, who spoke to reporters Wednesday as he was leaving jail, denied the charges and said, "I've been sober for 10 years."
In 1992, Rich entered a drug rehabilitation program after pleading no contest to felony burglary and drug charges alleging he stole a drug-filled syringe from a hospital and broke into a pharmacy.
In 1988, Rich entered the Betty Ford Clinic for treatment of cocaine addiction. He had been kicked out of another rehabilitation program elsewhere after demanding painkillers.