Rodriguez and the A's have already come to terms on a one-year deal, per a team announcement. Details of the contract are not known, but MLBTradeRumors.com projected a $500,000 salary for the right-hander in 2014.
Rodriguez, 29, has a career 4.89 ERA, but also 136 strikeouts in 123 1/3 innings spanning 119 big league appearances. He has yet to throw a pitch for the A's after missing all of the 2013 season while recovering from Tommy John surgery, performed just weeks after he was traded to Oakland in February.
Rodriguez ensures the A's of bullpen depth, which is typically on the wish list of every team around this time of year, but even more so for Oakland at the moment, with free-agent closer Grant Balfour expected to sign elsewhere.
Depth stands as reason to keep Barton, as there are scarce options at first base behind the platoon duo of Moss and Nate Freiman in the higher levels of Oakland's Minor League system.
Barton, 28, has long been considered a great defender, and the A's still like his ability to get on base. He hit .269/.350/.375 with three home runs and 16 RBIs in 37 games for the A's this past season, after combining for just one homer, 27 RBIs and a .208 batting average in 113 games over the previous two seasons.
Last year, the A's tendered Barton a contract, but it was non-guaranteed, and they could choose to go the same route again. MLBTradeRumors.com predicts his 2014 salary to be $1.4 million.
Other predicted salaries: Lowrie, $4.8 million; Smith, $4.3 million; Moss, $3.8 million; Jaso, $2.2 million; Reddick, $2.2 million; Blevins, $1.5 million; Chavez, $600,000. That accounts for $19.4 million, to be added to the nearly $34 million already committed to five players for 2014.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.