There is a way. I've never heard of anyone doing this before, but it could make you some money depending on who your audience is and your willingness to market ads.
Trying to sell anyone anything these days is pretty much the-kiss-of-death. People are too distracted by and resentful of advertising.
However, just getting a name (a product name probably) in the public eye without a sales message is valuable. The goal of this is what they call "product recognition".
If in your game world, there were a place for a billboard or a car bumper, you could place a simple message there, just the name of a politician running for office or just the name of a product. You don't want something attention grabbing. You would want something barely noticeable. You want the name in the background not in the foreground. In the case of a politician, you could customize the name to the user's location. Perhaps there is some other place within your game where you could place a name.
The problem all side projects face is "marketing". The product is usually much easier to come by than a way to reach you customers. In your case the problem would be doubled because you need to both market to game players and market the ads to someone.
Good luck!