The Dodgers also put Enrique Hernandez on the injured list with a sprained left hand Monday.
Rosscup is headed to his fourth team this season.
Rosscup finished last season with Los Angeles, but was designated for assignment in November. He signed with Seattle, but was designated for assignment May 17.
Toronto claimed Rosscup off waivers, but designated him for assignment May 28 after two appearances. He re-signed with the Dodgers last month and made seven appearances, but was designated for assignment two weeks ago.
Rosscup is 2-0 with a 5.00 ERA in 28 combined appearances this season. He likely will join the Cardinals' Triple-A affiliate in Memphis.