Smith was among the Lions' final cuts just before the season.
Detroit originally acquired him from the Denver Broncos two years ago for tight end Dan Gronkowski. Smith had three interceptions in 11 games last season, including one start, and has eight interceptions in his three-year career.
Williams had just two carries for 3 yards this season. He has run for 459 yards and five touchdowns in two-plus seasons with the Lions and Washington Redskins.