Rice has been elevated from the practice squad amid a series of moves Tuesday, Chris Brown of the Bills' official site reports.
Rice has floated around the league for a few years now, so the last month of the season will be an important audition if he's to find a more permanent home in the NFL, as his practice-squad eligibility is starting to come to a close.
Rice was waived by the Browns on Wednesday, Nate Ulrich of the Akron Beacon Journal reports.
Rice had played only 37 defensive snaps across eight games this season, mostly serving as a special teams player. The Browns claimed cornerback Phillip Gaines and safety Jermaine Whitehead off waivers to prompt his departure from the team.
The Browns signed Rice to a reserve/future contract Wednesday.
Rice is entering his fourth year in the NFL but didn't appear in a regular-season game in 2017, though he did spend time on the Colts' practice squad during the second half of the season. He slots in as the 10th member of the Browns' current cornerback corps and faces an uphill battle to secure a roster spot in advance of the 2018 campaign.