Left-hander Felix Doubront, acquired in a trade with the Red Sox on Wednesday, was placed on the 15-day disabled list with a left calf strain, which allowed the Cubs to recall Parker.
The Cubs selected the contract of Valaika from Iowa. A non-roster invitee this spring, Valaika, 28, played in the Major Leagues last season with the Marlins, batting .219 in 22 games. In 102 games at Iowa, he was batting .278 with 10 home runs, 21 doubles, and 50 RBIs. He has played every position except catcher this season with the Minor League team.
Parker, 29, has pitched in seven games with the Cubs in his previous stints, and given up six earned runs over 9 2/3 innings. He has 21 saves at Iowa. The right-hander was optioned to the Minor League team on Wednesday, but was able to return because of the injury to Doubront.
Russell and Bonifacio were dealt Thursday to the Braves for Minor League catching prospect Victor Caratini.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.