Barrett has been suspended for one game after he was stopped at a Columbus police check point early Saturday morning.
Records show an arraignment scheduled for Friday morning in Franklin County Municipal Court. The records don't indicate if Barrett has a lawyer who could comment on the citation.
The 20-year-old Barrett took over as the full-time starter for the top-ranked Buckeyes on Oct. 24, throwing for 223 yards and three touchdowns in a 49-7 win over Rutgers.
Ohio State had a bye last weekend and will host Minnesota on Saturday.