The River Cats announced the deal Monday on their Twitter account.
Blanton, 33, became available when the Los Angeles Angels released him late last week. He was a major disappointment in Los Angeles, going 2-14 with a 6.04 ERA last season after signing a two-year, $15 million contract with the Angels as a free agent.
The Angels gave Blanton a chance to reassert himself in spring training, but released him after he gave up 16 earned runs in 20 1/3 innings in the Cactus League.
Blanton began his professional career as a first-round draft pick by the Athletics out of the University of Kentucky in 2002. He posted a 42-34 record and averaged 208 innings per season from 2005-2007. The Athletics traded him to Philadelphia for pitcher Josh Outman and two other players in December 2008.
Blanton is expected to provide depth for an Oakland rotation that has been weakened by injury this spring. Jarrod Parker, who had projected as Oakland's Opening Day starter, underwent Tommy John surgery last week, and A.J. Griffin began the season on the disabled list with flexor tendinitis.
The Angels reportedly are still on the hook for almost all of the $8.5 million still owed Blanton.