Rasmus, who reportedly has had differences with Cardinals Manager Tony La Russa, was sent to the Blue Jays in exchange for Jackson, who had been traded to Toronto from the Chicago White Sox only a few hours earlier.
Rasmus, 24, was hitting .246 with 11 homers with 40 runs batted in this season after belting 23 homers last year and 16 during his 2009 rookie season.
Jackson, meanwhile, has compiled a 7-7 mark with a 3.92 ERA in 19 starts for the White Sox, but he became the odd man out in Chicago's rotation and is eligible for free agency after the season.
The Cardinals also received outfielder Corey Patterson and pitchers Marc Rzepczynski and Octavio Dotel from Toronto while the Blue Jays picked up pitchers P.J. Walters, Brian Tallet and Trever Miller from St. Louis.
The White Sox had earlier obtained pitcher Jason Frasor and pitching prospect Zach Stewart for Toronto in exchange for Jackson and infielder Mark Teahen.
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