Dennard started seven games as a rookie in 2012 and nine in his second season. He started four of the first seven games last season but played in only two more and went on injured reserve with a hamstring injury before the last game of the regular season.
In 29 games with the Patriots, he had five interceptions.
Dennard was drafted in the seventh round out of Nebraska after being arrested for assaulting a police officer. He was found guilty in February 2013.
The Patriots also cut long snapper Tyler Ott and linebacker Deontae Skinner.