Rincon has not appeared in any games this season, but batted .285 in six seasons in the Padres organization. He never played above Double-A.
To make room for Rincon on the Royals' 40-man roster, pitcher Nate Adcock was designated for assignment. Adcock is 3-4 with a 7.09 ERA in 10 games and nine starts this season for the Triple-A Omaha Storm Chasers.
In other Storm Chasers news, pitcher Danny Duffy and center fielder Jarrod Dyson began rehab assignments with the team on Thursday.
Duffy, recovering from Tommy John surgery last June, made three starts for Double-A Northwest Arkansas, where he was 0-2 with a 4.22 ERA. Dyson is recovering from a high ankle sprain he sustained on May 16. He started four of the six games before his injury and was beginning to get consistent playing time when he was hurt. He was batting .268.