Dugger was claimed off waivers by the Reds on Wednesday.
Dugger made his Rays debut Sunday against Minnesota and allowed three runs while striking out seven in 5.1 relief innings. After being designated for assignment Monday, the right-hander will find a new home with the Reds. He doesn't have any options remaining, so he'll presumably join the major-league roster and is a candidate to start one of the two games in Saturday's doubleheader against Pittsburgh.