The charge was announced during his hearing at the Los Angeles County Superior Court earlier Monday, his lawyer Blair Berk said.
Randolph, who was arrested and booked on suspicion of DUI on April 6, was suspended for two games because of the incident.
He was pulled over at 2:25 a.m. when two California Highway Patrol officers saw his white Rolls-Royce weaving on Interstate 405.
The officers pulled the car over and said alcohol could be smelled inside the car. After conducting a field sobriety test, the officers arrested Randolph and took him to the Men's Central Jail in downtown Los Angeles.
Randolph did not appear at the hearing on Monday, but he put in a not guilty plea for the reckless driving count.
He is set to appear in court in early May.