Unless there is a law in your state stating expressively that you have to, no. I doubt that there is such a law.
If there is a law in your state that makes possession of a fraudulent or ficticious DL or ID a crime, and such a law exists in most states, then you probably could.
A California court has decided that you actually could make a "citizen's arrest" and confiscate the fake ID if it is in plain view (which it would be since the person presented it to you) until police arrives. I have not researched any other states, though.
You are not authorized to search a person, though, even if you make a citizen's arrest.
The court did not address the question if you can "only" confiscate the ID without arresting and holding the offender until police arrives. I guess you probably could and probably the offender would not complain, but these are uncharted waters.
So normally as a private citizen you are not forced to be a cop and do their work.
