Borchard, 24, struggled in his second stint at the big league level, batting just .184 (9-49), with 18 strikeouts, five RBIs and one homer in 16 games. Borchard played 16 games last season as a September call-up and batted .222 with two home runs, five RBIs and 14 strikeouts.
Borchard was drafted by the Sox in the first round of the 1998 draft, receiving a $5 million signing bonus, which was done to keep him from staying at Stanford and play football. Borchard was drafted in 1997 by the Baltimore Orioles, but failed to sign.
The 26-year-old Rivera went 9-53 with the Padres in 19 games this season. Rivera, who began his career with the Tigers in 2001, was traded to San Diego this past off-season. In four games in 2001, Rivera went 4-12 with with a RBI. Rivera batted .227 with one homer and 11 RBIs in 39 games in 2002.
The Sox have not announced who will take the place of Borchard, but all signs point to either Willie Harris, who was placed on the 15-day disabled list on May 22 with a shoulder injury, or Aaron Rowand, who started the season in centerfielder before getting demoted to Charlotte.