Soto was expected to be in uniform Tuesday night against the Los Angeles Angels. To make room on the roster, the Rangers designated catcher Yorvit Torrealba (yohr-VEET' tohr-ee-AL'-bah) for assignment.
The 29-year-old Soto was the NL rookie of the year in 2008, when he hit .285 with 23 home runs. But he hit just .199 with six homers and 14 RBIs in 52 games for the Cubs this season.
Torrealba hit .236 in 49 games in his second season with the Rangers.
Brigham was 5-5 with a 4.28 ERA in 21 starts for Double-A Frisco. He was a sixth-round pick by Texas in 2006.