Starks signed a one-year franchise tag with Miami in 2013 after making the Pro Bowl the prior season.
However, he wanted long-term security with the Dolphins and expressed unhappiness with the tag heading into training camp. That quickly put Starks out of favor with the coaches.
The Dolphins made Starks a rotational defensive tackle, and he came off the bench behind Jared Odrick and Paul Soliai. He finished with 49 tackles and four sacks. Miami's run defense ranked 26th in the league.
ESPN.com Dolphins reporter James Walker contributed to this report.