In a corresponding move, outfielder Dayan Viciedo was designated for assignment.
Beckham, 28, was a 2008 first-round draft pick of the White Sox and spent the first five-and-a-half seasons of his MLB career in Chicago. He was traded to the Los Angeles Angels in August for cash and a player to be named.
In 127 total games last season, Beckham hit .226 with nine home runs, 44 RBIs and a .618 OPS.
"Adding Gordon improves the depth and flexibility of our roster," White Sox general manager Rick Hahn said in a release. "We are thrilled to have him back. Like Emilio Bonifacio, Gordon brings the ability to play solid defense at multiple positions or play on an everyday basis should the need arise. This also gives Robin the ability to play matchups more effectively when setting the lineup."
Gordon has spent most of his career at second base (628 games), but has also played third base (112 games) and shortstop (seven games). He owns the second (.9899 in 2012) and third (.9889 in 2011) highest fielding percentages by a White Sox second baseman in team history, trailing only Nellie Fox's .9901 mark in 1962.
Viciedo, 25, batted .231 with 21 home runs and 58 RBIs in 145 games with the White Sox last season. He originally signed with Chicago in December 2008.
- Mike Fiammetta