His deal had expired last week and he was an unrestricted free agent.
Mays is a 6-foot-3, 220-pounder who played in eight games with one start before ending his season with a dislocated shoulder suffered against the Detroit Lions.
The former San Francisco 49ers second-round draft pick from USC was acquired by the Bengals during a 2011 trade.
For his career, Mays has 50 games played and 10 starts with 79 tackles, a blocked punt recovered for a touchdwon, a forced fumble and four pass deflections.
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Aaron Wilson covers the Ravens for The Baltimore Sun