Criswell, 27, was 1-1 with a 5.40 ERA in nine relief appearances for the Rays earlier this season, including two outings in August. He has pitched at least two innings in each of his outings for Tampa Bay this season.
Ramirez, 33, was 1-0 with a 6.48 ERA in 15 appearances (two starts) for the Rays after he signed with the club as a free agent June 13. Ramirez allowed six runs (four earned) in three innings of relief work during Friday's 11-4 loss to the Toronto Blue Jays.
He is 40-45 with a 4.37 ERA over 314 appearances (96 starts) in 12 seasons for six teams.
Reuters contributed to this report.