The man, who has been identified as Robby Stratton, can be heard saying, "Y’all got beer still? Y’all ain't out, are y’all?"
The video shows him chase another person inside the store while people laugh in the background.
In the video, Stratton said the alligator he was holding was alive.
"I don't even remember coming up here,” Stratton told WJAX Saturday. "This store sells some good liquor and I drank a lot of it that night.”
Stratton told WJAX that he found the alligator in the back of the truck.
Karen Parker, a spokeswoman with FWC, said they were informed about the incident Friday through a tip via their wildlife alert number. Investigators still have to talk to witnesses and the people involved.