The trade was made Wednesday, the same day Patton was in the Triple-A All-Star game. The Rangers assigned him to Triple-A Round Rock.
Frasor was 1-1 with a 3.34 ERA in 38 appearances this season, his second in Texas. The right-hander spent nine seasons with Toronto (2004-12), returning to the Blue Jays after being traded to the White Sox in July 2011 and finishing that season in Chicago.
Rangers general manager Jon Daniels said catcher Geovany Soto will be activated from the disabled list before Friday's game at Toronto and set for his season debut in the majors after knee surgery.
The injury-plagued Rangers (38-57) went into the All-Star break with the worst record in the major leagues. They were 21 games behind AL West-leading Oakland.
Daniels said the deal with the Royals is ''just a good baseball trade and we like the return'' and not any indication that Texas will start unloading potential free-agent players, such as the 36-year-old Frasor.
''It's not necessarily related to anything else we may do,'' Daniels said. ''We're certainly going to listen. I think the closer guys are to free agency, it's just the more natural those conversations are to take place. But we're still going to make good baseball trades at this point.''
Kansas City (48-46) is second in the AL Central, 6 1/2 games behind Detroit.
To make room on their roster for Frasor, the Royals optioned Louis Coleman to Omaha and designated utility player Jimmy Paredes for assignment.
Patton is 4-3 with a 4.08 ERA and 14 saves in 34 relief appearances for Triple-A Omaha this season. The 26-year-old righty has 60 strikeouts in 46 1-3 innings while holding opponents to a .161 batting average.
In 624 major league games, Frasor is 31-35 with 36 saves and a 3.65 ERA.
Soto had surgery for torn cartilage in his right knee after getting hurt near the end of spring training. Before that, he had been limited to only six spring games because of a surgical procedure on his left foot.
The Rangers acquired Soto from the Chicago Cubs at the non-waiver trading deadline in 2012. He hit .245 with nine homers in 54 games last season for the Rangers.
Soto was arrested last week and charged with misdemeanor possession of marijuana under two ounces after a traffic stop by police in Grapevine, Texas. He was released on $500 bail and has apologized to his family, the Rangers organization and fans.