Police tell ABC News that around 12:35 a.m., LaBeouf, 30, engaged in a verbal dispute with the man, a 25-year-old resident of the Bronx.
LaBeouf proceeded to pull the scarf of the other man, scratching his face while doing so. The actor also pushed the man, police said.
The unidentified man refused medical attention.
After police arrived, LaBeouf was taken into custody. He was charged and received a a desk appearance ticket for court at a later date.
It is unclear if LaBeouf has a lawyer. ABC News has contacted the actor's representatives for comment.
The project kicked off at 9 a.m. last Friday, when the actor and his performance art partners Nastja Säde Ronkko and Luke Turner placed a camera on a wall outside the Museum of the Moving Image in the New York City borough of Queens. The camera is intended to broadcast people shouting "He will not divide us!" over and over again.
A website for the project reads, "Open to all, 24 hours a day, seven days a week, the participatory performance will be live-streamed continuously for four years, or the duration of the presidency,” the project website reads. “In this way, the mantra “HE WILL NOT DIVIDE US” acts as a show of resistance or insistence, opposition or optimism, guided by the spirit of each individual participant and the community.”
WABC News' Mark Crudele contributed to this report.