Randall was the Dolphins' seventh-round pick last year and played in 12 games. He was waived by Miami on Aug. 31.
Atkins tore the ACL in his right knee during a 22-20 overtime loss in Miami last Thursday.
The Bengals put Atkins on injured reserve Monday and replaced him by signing defensive tackle Christo Bilukidi, a sixth-round pick of the Raiders last year. The deal was later voided by the NFL because Bilukidi didn't have a current work permit from Canada to keep playing in the United States after the Raiders waived him, so the Bengals signed Randall on Tuesday.