The Sunderland fan captured the nation’s heart during his battle with neuroblastoma, but succumbed to the illness aged six in 2017.
He was a mascot for his beloved club and, in the months before his death, led England out at Wembley alongside former Black Cats striker Jermain Defoe.
Pictures circulated on X, formerly Twitter, showed two men laughing at the Sheffield Wednesday v Sunderland match at Hillsborough on Friday, with one of them holding up a picture of Bradley to the camera.
Dale Houghton, 31, from Rotherham, was arrested on Saturday and has been charged with a public order offence, South Yorkshire Police said.
They said a second man also arrested on Saturday has been released on bail pending further inquiries.