Once in handcuffs, the redshirt sophomore did name-drop his position with the Buckeyes and asked if there was anything the officer could do to help him. The video, initially obtained by TMZ, also includes Barrett cursing to himself twice once he was put in the back of a police cruiser before telling officers that teammate Cardale Jones was coming to pick him up.
"I mean, I'm the quarterback at Ohio State," Barrett said at one point. "Officer, there isn't nothing you can do?"
The officer replied that his "intentions are not to take you to jail."
Barrett will pay a $400 fine and have his license suspended for six months after pleading guilty Tuesday to operating a vehicle under the influence, a misdemeanor.
In addition, Barrett, 20, must complete a three-day alcohol education program as a result of the incident, when he was stopped at a DUI checkpoint early on Oct. 31. He must complete the class and pay the fine by Feb. 15 or face jail time, Judge H. William Pollitt said as he accepted Barrett's plea.
"I'm just truly sorry," Barrett said in a brief statement at the time of the plea.
An additional charge of backing without safety was dismissed, and the case has been closed.
Barrett was home relaxing with friends when a "heavily intoxicated" friend stopped by and Barrett decided to drive him home, said Barrett's attorney, Phil Templeton, who wouldn't identify the friend.
The lawyer noted to the judge that Barrett's blood-alcohol level of 0.099 was only slightly above the legal limit of 0.08 for adults, though he acknowledged Barrett was underage. In Ohio, the limit is 0.02 for people under 21.
On the field, Barrett's situation for third-ranked Ohio State also has been resolved, as he is in line to return to the starting lineup for Saturday's game against Illinois.
"We are aware of the video," an Ohio State spokesperson said Thursday. "The events that prompted it have been addressed and we are moving on."
Barrett was suspended one game by coach Urban Meyer and lost his 2016 summer financial aid as a result of the OVI, and he watched the Buckeyes' 28-14 win over Minnesota last week from the press box. Jones started in his place, accounting for more than 250 total yards and protecting the team's undefeated record.
"I think [he handled it] well," Meyer said Monday. "It's a mistake made -- a serious mistake -- by a kid that's really lived most of his life mistake-free. He's a kid that's human, and I still have these conversations with him.
"You can handle when people say you're not very tall or fast enough or you don't throw far enough, but when someone challenges who you are as a person or a man, that's tough. He's probably not had that happen to him very often."
The Associated Press contributed to this report.