Williams, 26, wound up going undrafted out of Tennessee back in 2015. He has played for the Jets, Dolphins and Giants since entering the NFL.
For his career, Williams has appeared in two games and recorded two tackles.
Crawford, 22, wound up signing on with the Titans as an undrafted free agent out of Indiana back in May. He agreed to a three-year, $1.755 million contract but was waived soon after.
The Titans signed Crawford to a contract last week.
During his college career at Indiana, Crawford recorded 276 tackles, two sacks, nine interceptions, a defensive touchdown, three forced fumbles, five recoveries and 19 pass defenses over the course of four seasons and 50 games.