Of course, with such a high-profile player heading for the open market (or at least a somewhat open market), the rumor mill is cranking away, spitting out names of teams thought to be interested in Moss' services. The Rams, of course, being a bit on the thin side at the wide receiver position (and thin is being polite; I thought describing them as anorexic at the wide receiver position might not go over well), have been listed high among the ranks of possible landing spots.
Currently Danny Amendola is the Rams' number one option at receiver, and as much as I love Amendola his role really shouldn't be as your top threat. I like Brandon Gibson as a possession guy, but he's really a number three. Laurent Robinson shouldn't be on the field. Let's face it: the Rams' receiver situation is dire.
Moss would immediately present a deep-ball threat the Rams have really only had on the field for the one game Alexander was healthy and playing. He certainly isn't the Randy Moss of old, but there is still plenty of physical talent left there. So yes, he would fit very well on this team in terms of adding a wide receiver.
Unfortunately, that's only half the story with Moss. Personally, I've never seen him as the same cancer in the clubhouse a guy like Terrell Owens is; Moss is plenty antisocial in his own way, of course, but he doesn't rip apart teams with his antics the way T.O. has in the past. At the same time I say that, though, it's also very true Moss is far less than an ideal citizen most of the time. When he's happy and motivated Moss is one of the greatest receivers to ever strap on a helmet. When he's pouting and dissatisfied, Moss has proven in the past he is willing to quit on a team.
Personally, as much as I wish the Rams could find some sort of receiver upgrade this season, I just don't think Moss would be a very good idea. Steve Spagnuolo and the rest of his staff finally have this club pointed in the right direction; I don't know the potential strife of having a discontented Randy Moss in the locker room would be worth what he might bring on the field.
The Rams aren't a title contender this year. They're a much better team than in the past, but are really only in contention in the NFC West because of their weak schedule and the general awfulness of the division. They seem to have a good locker room. All the players are pulling in the same direction. Bringing in Randy Moss isn't going to put them over the hump, but it could very well set this team back to have a malcontent hanging around the young players.
So yes, to answer the question posed in the title, Randy Moss could be a fit for the Rams. Whether he would be a good enough fit to offset all the baggage he's carrying along with him is another question, though. And on that count I just don't think he would be.