In corresponding roster moves, the Cubs optioned pitchers Kyle Hendricks and Blake Parker to Iowa.
Barney is hitting .224 with two home runs and 16 RBI in 70 games for the Cubs this season. He was placed on the paternity leave list on Wednesday.
Rosscup has made four scoreless appearances for the Cubs this season.
Hendricks made his big league debut on Thursday, allowing four runs on five hits over six innings in Chicago's 6-4, 12-inning win at Cincinnati.
Parker is 1-0 with a 9.53 ERA in five games for the Cubs this season.