Briscoe underwent knee surgery last month, and the move will allow Carter-Williams to be eligible for the playoffs should Orlando qualify. Carter-Williams had previously signed two 10-day contracts with the Magic under a hardship provision.
The Magic signed Briscoe to a three-year, $3.9 million contract in July, but Orlando will have no cap obligations past this season as the 2019-20 and 2020-21 seasons were non-guaranteed.
Briscoe went undrafted in 2017 after leaving Kentucky following his sophomore year. He made his NBA debut this season and in 39 games averaged 3.5 points in 14.3 minutes per game.
He is eligible to be claimed but only by a team that has a trade exception for $838,000.
ESPN's Bobby Marks contributed to this report.