Tomko was designated for assignment on Thursday after being rocked by the Texas Rangers in the ninth inning of an 11-5 loss on Wednesday night.
Rosa was promoted from Triple-A Omaha where he was 2-1 with a 3.96 ERA in five starts. He was assigned to the bullpen by the Royals.
Manager Trey Hillman, asked about how Rosa will be used, replied: "Get outs when we give him the ball because we've had trouble doing that with the exception of three or four guys."
Rosa began the season with Double-A Northwest Arkansas and posted a 4-2 record with a 1.20 ERA in eight starts. In his two Minor League assignments combined, he had 62 strikeouts and just 11 walks in 70 innings.
"There's some deceptiveness to go with the ball jumping out of his hand," Hillman said. "I like the way he spins the ball. He threw strikes with it at Spring Training. The other thing that sticks out is he wasn't afraid to pitch inside."
The bullpen, one of the club's strong points early this season, has been struggling. In successive games against the Rangers, the relievers blew 5-1 leads.
Tomko was signed to a one-year, $3 million contract last January.
He was assigned to the bullpen after being unable to win as a starter. In 16 games, including 10 starts, he had a 2-7 record and a 6.97 ERA. Opponents hit .317 against him and he gave up 11 home runs.
There's a 10-day period in which Tomko can be placed on waivers, traded, released or accept a Minor League assignment.
"Maybe it'll be better," Tomko said. "It happened last year and I pitched great. A change of scenery might be good."
Late last season, Tomko was released by the Los Angeles Dodgers, retooled his pitching delivery, then signed with the San Diego Padres for a successful September.
In the ninth inning on Wednesday night, he gave up three runs on five hits including David Murphy's home run. One line drive came close to his head.
"That's the closest I've ever come to being hit in the face. I felt the ball go by my face," Tomko said.
Tomko was bumped to the bullpen after a 7-2 loss at Toronto on May 26 that dropped his record to 2-6.
"I'm not sure I've ever seen it go south as it went for Brett, as quickly as it did," Hillman said. "Last night was a perfect example. He was still throwing the ball 93, 94 miles an hour, but location matters and [he had the] inability to locate in non-dangerous areas, to keep it from snowballing."
A veteran of 12 Major League seasons, Tomko was a gracious clubhouse presence and an artist of some note. Recently he completed a painting of fellow pitcher Joakim Soria to be auctioned at an upcoming Royals charity event.
Tomko didn't forget. Just before leaving he reminded a Royals official to get the finishing touch for the painting.
"Just have Soria sign that," he said.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.