LaBeouf approached a bystander and a police officer and when no one would provide him with a cigarette, he became disorderly "using profanities and vulgar language in front of the women and children present", according to the report.
The 31-year-old then became aggressive towards the officer and ran to a nearby hotel when the officer tried to arrest him. He was then arrested at the hotel after additional disorderly behaviour, police said.
LaBeouf was taken into custody and his name has since showed up on the Chatham County Sheriff's Office book log.
According to TMZ, LaBeouf was in police custody in Georgia until 11am (1am AEST), when he was released on $US3500 ($4600) bail.
He is currently filming indie movie The Peanut Butter Falcon in Savannah, which co-stars Dakota Johnson and Bruce Dern.
According to several local residents on Twitter, LaBeouf was seen having dinner with Johnson earlier in the evening before continuing his partying into the early morning hours.
It's the latest in a string of run-ins with the law; LaBeouf was also arrested in January at his anti-Donald Trump art installation, where he was charged with misdemeanour assault.
He was arrested in October 2015 in Austin, Texas, also for being drunk in public and running through the streets of the city.
LaBeouf was also booked for drink-driving in 2008.