Feed and water the pigeon
In this case it is best to feed and water the pigeon and give it time to rest naturally, as long as it is not injured and is safe from predators.
Because racing pigeons are domesticated birds they will respond better to being handled and nursed than most wild birds. You can feed the pigeon with corn, dry uncooked rice, lentils, or special pigeon food and importantly provide the pigeon with water.
After a couple of day's rest an uninjured bird will usually recover enough to continue on it's way home.