Colorado acquired Givens in a deal with Baltimore on Aug. 30. He allowed at least a run in five of 10 appearances for the Rockies.
Givens appeared in 12 games for the Orioles before the trade and allowed two runs over 13 innings. Combined, he was 1-1 with a 3.61 ERA with Colorado and Baltimore.
He turns 31 on May 13.
Givens was selected by the Orioles in the second round of the 2009 amateur draft. He is 21-17 with a 3.41 ERA and 21 saves over 345⅓ innings during his career. Givens was due to make $3,225,000 in 2020 and his prorated salary wound up at $1,194,444.
Six Rockies remain eligible to exchange proposed arbitration salaries on Friday: right-handers Carlos Estevez, Jon Gray and Robert Stephenson, left-hander Kyle Freeland, second baseman Ryan McMahon and outfielder Raimel Tapia.