If it's a Rock Dove (Columba livia), "common pigeon", you can pretty much do whatever you want in the US. They're one of the few species not protected under the Migratory Bird Treaty Act (MBTA) here. However, there are a number of species variants that are still known as "pigeons", within the Columbidae family. Also, keep in mind that Mexico, Japan and Russia have also ratified the MBTA to some degree. There will be regional legal variations that I'm not aware of. I doubt they're protected in those countries, but I've never looked into it. Species that are considered "game" in a country may have specific regulations or permits required to "take" them.
long story short-What they said, get a cat, let them fledge, or call your local animal control. If they're the usual suspects that i'm aware of "common pigeon", or the Eurasian collared dove, what Marburg said, minus the promise to not shoot em. Nasty little bastards, whose populations are getting out of control.
