The A's did not immediately make a corresponding move, though it's expected that catcher Josh Phegley, currently on the seven-day concussion DL, will be activated and take his roster spot Friday in Texas.
Cotton, who opened the season in the third spot of the rotation, pitched well at times, but also gave up at least five runs in three of his seven outings, yielding a 3-4 record and 5.68 ERA.
Most recently, the right-hander took a loss against the Angels on Tuesday after allowing seven runs on eight hits, including three home runs.
Cotton's 35 strikeouts lead Major League rookies, and his 38 innings pitched are tops among American League rookies, but command often escaped the young pitcher, an issue he'll be allowed to harness at the Minor League level.
Cotton, 25, came to the A's in last year's deal with the Dodgers that sent Josh Reddick and Rich Hill to Los Angeles.
Jane Lee has covered the A's for MLB.com since 2010. This story was not subject to the approval of Major League Baseball or its clubs.