Stevenson agreed to terms on a three-year, $2.325 million contract with Washington on Tuesday.
Stevenson was sent down to AHL Hershey on Tuesday, Tarik El-Bashir of Monumental Sports Network reports.
Stevenson was recalled from AHL Hershey on Monday.
Stevenson was reassigned to AHL Hershey on Saturday.
The Capitals called up Stevenson from AHL Hershey on Friday.
Stevenson had successful surgery on his right hand.