The left-hander was 1-1 with a 2.59 earned run average in 15 relief appearances with the Royals, who signed him as a minor league free agent on May 21 after he was released in spring training by Seattle.
Ramirez is 39-30 with a 4.30 ERA, including 104 starts, in the majors with Atlanta, Seattle and Kansas City.
"I've got mixed emotions, but I think it will be fun," Ramirez said. "I've been lucky enough to be part of a couple of [playoff races] in Atlanta. It's definitely a fun part of the year."
The White Sox added Ramirez after a game in which their bullpen imploded in a 6-2 loss to the Red Sox. Reliever Boone Logan allowed four runs without recording an out, and was told after the game that he'd be sent to the minors before Sunday's game.
Orlando was hitting .264 with 15 doubles, 12 triples, nine home runs, 42 RBIs, 73 runs and 28 stolen bases in 37 attempts with Class A Winston-Salem in the Carolina League. The Royals assigned the 22-year-old to Class A Wilmington. Orlando, from Brazil, has stolen 77 bases in 2½ seasons in the White Sox organization.
Newman, who went to Ohio State, made eight relief appearances earlier this season with Colorado and had a 9.35 ERA, allowing nine runs and 15 hits in 8 2/3 innings.