"Billy will be a nice running option for us, plays the outfield well," manager Bob Melvin said of Burns, who has 54 steals in the Minors this year and has appeared in three games for Oakland.
Rodriguez appeared in six games with the A's in May and allowed one run in eight innings. Anderson, who bats left-handed was traded to the A's from the Reds on Aug. 24, has hit .210 in 62 big league at-bats.
The A's designated left-hander Joe Savery for assignment to make room for Anderson on the 40-man roster.
Aaron Leibowitz is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.