Garcia was 4-0 with a 2.67 ERA in five starts for Triple-A Norfolk this season. He was named International League Player of the Week for the week ending April 28 after going 2-0 with a 1.69 ERA in 16 innings.
Garcia's 152 career victories rank ninth among active pitchers, and he has the most wins for any Venezuelan-born pitcher in baseball history. He's gone 6-3 with a 3.28 ERA in 10 career postseason starts, including seven innings in the clinching Game 4 of the 2005 World Series for the White Sox.
Garcia will wear No. 38.
Clark, 29, made his major league debut Wednesday in Seattle and allowed three runs and three hits in 1 2/3 innings, with two walks and one strikeout. He went 1-2 with a 4.56 ERA in five starts with the Tides this season.
Clark went 15-7 with a 2.79 ERA in 28 games (26 starts) with Double-A Bowie and Norfolk in 2012.
Also, catcher Luis Exposito cleared waivers and was outrighted to Norfolk. The Orioles designated him to make room for catcher Chris Snyder.