Givens, 31, was 3-2 with a 2.73 ERA in 31 appearances. He was drafted by the Baltimore Orioles in the second round in 2009 and made his big-league debut with the Orioles in 2015. He pitched six seasons with Baltimore before being traded to the Rockies in August 2020.
Davis, 24, an 11th-round pick in 2018, has pitched all season with the Dayton Dragons. He was 3-6 with a 3.60 ERA in 13 starts.
Williams, 19, a fourth-round pick in 2020, was pitching for the Single-A Daytona Tortugas. He was 2-5 with a 5.55 ERA in 11 starts and one relief appearance.
Earlier Wednesday, the Reds announced a trade with the New York Yankees, bringing right-hander Luis Cessa and left-hander Justin Wilson, who have combined to make 50 appearances for the Yankees this season, to Cincinnati for a player to be named later.
To make room on the roster for Givens, Cessa and Wilson, the Reds designated for assignment pitchers Edgar García, Ashton Goudeau and Josh Osich.
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