Rodgers was targeted twice in the passing game but had no receptions in Sunday's loss at Jacksonville.
Indianapolis signed Rodgers from its practice squad Tuesday.
The Colts elevated Rodgers to the active roster ahead of Sunday's game against the Rams, Adam Schefter of ESPN reports.
Rodgers was waived by the Colts on Tuesday, Joel A. Erickson of The Indianapolis Star reports.
Rodgers agreed to terms with the Colts on Wednesday.
Rodgers was waived by the Texans on Sunday.
Rodgers caught three of four targets for 22 yards in a 32-31 victory over Indianapolis in Week 18.
Rodgers caught both of his targets for 12 yards and ran once for four yards in Sunday's 31-3 loss to the Jaguars in Week 17.
Rodgers caught one of two targets for 37 yards in Saturday's 19-14 win over Tennessee in Week 16.
Rodgers caught two of three targets for 26 yards in Sunday's 30-24 overtime loss to the Chiefs in Week 15.