Miami (6-5) is thin at cornerback with injuries to starter Cortland Finnegan (ankle) and second-year reserve Jamar Taylor (shoulder). Jones is a former seventh-round pick of the Dolphins in 2013 who is familiar with the defensive system. He was cut by Miami following training camp in August.
Jones also is solid on special teams and could help Miami in that area. To make room for the move, the team cut reserve cornerback Lowell Rose.
The Patriots host the Dolphins on Dec. 14.