Rivers began the season with the New York Knicks, who traded him to the Oklahoma City Thunder at the deadline. He was then subsequently waived. Rivers, 28, is averaging 7.3 points and shooting 36.4% from beyond the arc in 21 appearances this season.
The Nuggets are looking to replace the production of Jamal Murray, who suffered a season-ending torn ACL against the Golden State Warriors on Monday. Denver also has guards Facundo Campazzo and Monte Morris on the roster.
The Nuggets are currently fourth in the Western Conference with a 34-20 record entering Wednesday's slate of games.