Preheat the Dutch oven while dicing the onion and celery.
Add the oil, rice, onions, celery, and baby carrots to the Dutch oven. Stir while cooking until lightly browned.
Add the orange zest and juice along with the chicken stock, stir to combine then simmer for 20 minutes.
Add to the Dutch oven the salt, garlic, pepper, and cans of mandarin oranges including the juice. Stir to combine then add the game hens evenly in the Dutch oven. Gently wiggle the hens to sink them down into the rice and vegetable mix.
Place the lid on the Dutch oven then return back over the heat. Bring to a simmer and cook for 20 minutes. It is best to check the internal temperature which should be about 165 degrees F (75 degrees C) as the chickens are effectively being boiled/steamed and will not brown, giving the appearance they are not cooked.
Serve the whole game hens for a spectacular meal on a platter to get the full effect, or cut in half and serve as a normal-sized portion.