The wide receiver was claimed off waivers by the NFC West side after being released by the Detroit Lions earlier this month.
A statement by Rams coach Jeff Fisher said: "We felt that he was not the best option for us at the position.
"We saw Titus as an outstanding young player. The things that took place in Detroit were well documented from a media standpoint.
"We spent probably four or five days with him. At the end of the interview process, we decided it was best for us to go a different direction."
The 23-year-old scored four touchdowns for the Lions in 2012, missing much of the season because of discipline issues.