The news was first reported by Eleven Warriors, which reports that Baugh has also been suspended from team activities.
Per the police report, Baugh's most recent incident occurred Jan. 17 near the intersections of West 5th Avenue and Dennison Avenue. His arraignment is scheduled for Jan. 27.
Previously, Baugh received a one-game suspension and lost his summer financial aid after facing the same charge, as well as a charge of possessing fake identification. He eventually pleaded guilty to the first charge, but the latter was dismissed.
Baugh was a four-star member of the class of 2013 from Riverside, Calif., who was ranked the No. 3 tight end in the nation by Scout.com coming out of high school.
His teammates rallied to his defense after his original incident over the summer.
"He had a little hiccup. It happens," said Nick Vannett, his team-issued "big brother" on the team. "You're young. He just came in (to OSU). He knows the expectations, so there's no issue."
"Marcus is coming along really well," tight ends coach Tim Hinton said in September. "The honest truth is, he has not caught the ball as well as we want him to at this point in the year. He's a very athletic kid. He does really well on the field that way, but he just has not caught the ball as cleanly as he needs to and as consistently, and as he learns that skill, he'll be okay.
"I mean, he'll do well here. We knew coming in, he was more of a wide receiver tight end than a tight end. So his blocking skills obviously need to improve yet, but he has not caught the ball as cleanly as you need to, and I'll guarantee you, it's been emphasized in a certain room."