Rodgers-Cromartie, who worked out for the Raiders on Wednesday, also received interest from the Los Angeles Chargers and Seattle Seahawks.
The 32-year-old joins a secondary that includes offseason acquisition Rashaan Melvin, Leon Hall, Daryl Worley, Shareece Wright, Rick Nelson and Gareon Conley, who missed the majority of his rookie season with a hip strain.
Rodgers-Cromartie was released by the New York Giants in March after spending four seasons with the club. The two-time Pro Bowl selection started five of the 15 games in which he played last season and failed to record an interception for the second time in his career.
The one contest Rodgers-Cromartie missed was due to a suspension stemming from a violation of team rules. Per ESPN's Jordan Raanan, Rodgers-Cromartie nearly left the stadium during an October loss to the Chargers, and he later walked out of a defensive meeting at the team facility.
Listed at 6-foot-2 and 203 pounds, Rodgers-Cromartie had 48 tackles last season with the Giants. He has 30 interceptions -- including six for touchdowns -- in 10 seasons with the Cardinals, Philadelphia Eagles, Denver Broncos and Giants since being selected with the 16th overall pick of the 2008 NFL Draft by Arizona.