According to the California Highway Patrol, the 30-year-old was in a white Dodge sedan driving more than 100 mph on the 101 Freeway in Woodland Hills.
Officers "observed objective signs and symptoms of alcohol impairment," according to CHP.
The arrest came hours after he caught a touchdown in the Rams' loss to the Philadelphia Eagles on "Sunday Night Football."
Robinson was cited and released to "a responsible party," the CHP said.
Rams coach Sean McVay said he's still gathering information and hasn't decided whether Robinson will play Sunday against the Saints.
"Obviously, we expect better from him and we want to continue to gather all the appropriate information," he said. "I do believe that Demarcus has a good heart and never would have any ill intentions, and clearly there was a decision that's not in alignment with the things that we want to be about. I know he was remorseful about that.
"I don't think this makes him a horrible human. I think he made a bad decision and I think we are fortunate that there weren't anything ... there wasn't anything else that occurred as it relates to affecting anybody else in a negative way or himself from just an overall safety and health perspective."
Robinson is in his eighth NFL season and second in L.A. He has 26 catches for 384 yards and six touchdowns this season.
The incident remains under investigation.
ESPN contributed to this report.