During Monday night's game against the Kansas City Royals, Beckham used his foot to write "GETZ IS GAY! G.B.," near his position at second. Royals second baseman Chris Getz is a friend and former White Sox teammate of Beckham.
Fans in the upper deck were able to see Beckham's message clearly, and at least one photograph of the message is circulating on the Internet.
"Obviously I apologize and kind of want to move on," Beckham said Saturday. "Obviously it was meant as a joke but obviously it was in the wrong place and I didn't mean it that way. I will just try to move on."
Beckham has underachieved this season, batting .241 with 24 RBIs, though his defense has been much improved. He started the season in the No. 2 spot in the lineup but has been batting toward the bottom of the order most of the year.
"There just needs to be a greater awareness of when you're in the public eye," White Sox general manager Kenny Williams told the Chicago Sun-Times. "Something between two friends meant as a joke? Well, you're representing not just yourself, but your team, your sport, your family.''
"I'm disappointed,'' Williams continued to the Sun-Times. "I know Gordon, the man, and I can't think less of him because I do know him. And I know he and Getz are friends, but we traded Getz and Josh Fields in the offseason (before the 2010 season) for Mark Teahen.
The Sun-Times first reported the incident early Saturday morning.
Bryant used a gay slur in an April game after receiving a technical foul. He stormed to the bench, hit his seat before sitting down, threw a towel and then yelled "Bennie!" toward referee Bennie Adams. Bryant then leaned back and muttered a gay slur. NBA commissioner David Stern slammed Bryant with a $100,000 fine, and Bryant apologized the next day,
Noah was fined $50,000 for directing an gay slur at a fan during Game 3 of the Eastern Conference finals in late May.
Guillen was fined and ordered to undergo sensitivity training for using a similar slur in 2006 while referring to a former Chicago columnist.
"It's one of those things that was unfortunate that happened and I want to try to move on from it," Beckham said.
Doug Padilla covers the White Sox for ESPNChicago.com.