Defensive end Sam, who publicly revealed his sexuality in February, was chosen by the Rams in the seventh and final round of this year's draft after a fine collegiate career with the University of Missouri.
However, despite featuring heavily in the Rams' pre-season campaign, Sam failed to make the final cut for their regular-season roster after he was let go by St Louis on Saturday.
Sam could be claimed off the wavier wire by another NFL team, however, if he clears waivers, the Rams do have the option to sign him to their practice squad, which has been extended by the NFL from eight to 10 players.
Through four pre-season games Sam made 11 tackles and recorded three sacks.
The Rams will now turn their attentions to their regular -season opener with the Minnesota VIkings at the Edward Jones Dome a week on Sunday.