In the video, the men are laughing while the animal struggles and cries out in pain and distress.
Someone alerted The Exposed, who posted the video, which was posted on Snapchat.
Officers said Friday they believe the video was made in Arkansas by three Georgia residents and one Arkansas resident. Agents say they've questioned one of the individuals and plan to get statements from the other three within the next two days.
The investigation began after agents were contacted by the Georgia Department of Natural Resources.
According to the Arkansas Times, one of the men told police that the deer had been "hit by a car" and that they'd put it into the back of their car. Suddenly, they say the deer "regained consciousness" and so they apparently decided it would be funny to repeatedly beat it in the face with a heavy college textbook while they all laughed about it.
"It was disgusting. That's not reflective of Arkansas values, especially outdoorsmen and hunters. It was hard to watch," said Keith Stephens, with Arkansas Game and Fish.
The agency says the person seen beating the deer could be charged with a misdemeanor, fined up to $1,000 and get up to a year in jail under the state's criminal animal cruelty law.
The other three could face aiding and abetting criminal violations, which carry fines $250.
WARNING - VIDEO IS DISTRESSING:
(Valdosta Daily Times - Jan 29, 2016)