David Woodock, 38, of Barnsley Road, started talking to the youngster on Facebook before the pair arranged to meet in Sheffield in April 2019.
Judge David Dixon told those at Sheffield Crown Court that if she had been just months younger, Woodcock would have been facing a charge of rape rather than sexual activity with a child.
He added: “She has now started self-harming, cutting herself with a blade because of the five minutes you thought you were entitled to.
“I hope your selfish, arrogant and pathetic act was worth it, because that is what you have done to her, to her mum, to the rest of her family.”
Woodock was jailed for five years and two months.