Yes, that is the premise of Turd Birds, the newest game from 2K Games and developer Cat Daddy Games. This endless runner sees you as a bird that has to fly around levels and poop on people. You can even poop on pictures of your friends if you connect it with your Facebook profile.
You can poop different kinds of poop based on what you eat, utilize power-ups, and control different kinds of birds such as Sergeant Squirt and The Deuce. What the hell did I just write.
Turd Birds is a free download on the App Store, Google Play, and Amazon marketplace.