The altercation was captured on video.
Jones, who fought back after some initial hesitation, told the woman to "watch out" before punching Ragin.
Ryan Gaydos is an editor for Fox News.
During the fight, cops say Ragin also hit Pacman's female companion - injuring her hand.
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The video fails to follow the initial exchange, but then shows Jones landing a punch and knocking Ragin to the ground.
Jones declined medical treatment, police said.
Ragin, who was charged with two counts of battery, was transported to Grady Memorial Hospital to be treated for his injuries. Jones was suspended for the entire 2007 National Football League season and a portion of the 2008 season.
Most recently, in January 2017, Jones was arrested in Cincinatti for disorderly conduct, harassment with a bodily substance, and assault.
Pacman is now a free agent after the Bengals chose not to pick up their option on him for the 2018 season, and the 34-year-old defensive back doesn't now have a team for the upcoming season.