Minnesota asked Rincon on Thursday to accept the assignment, and his agent, Ed Setlik, said Friday he refused. The Twins cut the struggling right-hander before their game at Milwaukee and recalled third baseman Brian Buscher from their top farm club.
The Twins have 10 days to trade Rincon or he will become a free agent.
Rincon's salary this year is $2.475 million. The Twins are on the hook for the rest, unless they can agree in a trade to unload some of the money on another club.
After four straight seasons as a solid setup man, the 29-year-old Rincon lost his touch last year and his struggles intensified in 2008. His ERA was 6.11 over 28 innings, and he gave up 33 hits, 16 walks and five homers.
Also on Friday, the Twins signed their first-round draft pick, high school outfielder Aaron Hicks. He will be assigned to their Gulf Coast League team in Fort Myers, Fla.