Pounders, 26, had a 9.24 ERA in 13 games for the Royals last year and gave up six home runs in 12 2/3 innings.
Ruxer was a 12th-round pick by the Angels in 2014 out of Louisville.
Ruxer had a 3.08 combined ERA in Class A and Class A Advanced last year with 99 strikeouts in 111 innings.
Ruxer, 24, had Tommy John surgery during his senior year of college and did not pitch in 2014 after being drafted.
Jeffrey Flanagan has covered the Royals since 1991, and for MLB.com since 2015. Follow him on Twitter @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.