Pat the turkey dry and turn it breast-side down on a cutting board. Using sharp kitchen shears or a knife, cut the backbone out of the turkey, reserving it for stock. Flip the turkey so it's breast-side up, then press down on it with your hands to flatten the bird.
Whisk together the orange juice, oil, maple syrup and garlic in a large bowl. Reserve half of the marinade and set aside. Season the turkey on both sides with salt and pepper and place the turkey into the bowl with the marinade. Marinate in the refrigerator for 4 hours. Remove the turkey from the refrigerator an hour before grilling, so it can come to room temperature.
Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only on medium-high heat.
Place the turkey skin-side up over indirect heat and cover the grill. Maintaining a temperature of 375 to 400 degrees F, smoke the turkey until it reaches an internal temperature of 160 degrees F, about 90 minutes. Baste the turkey with the reserved marinade every 30 minutes during cooking.
Remove the turkey from the grill and rest, tented with aluminum foil, for at least 20 minutes before carving.
(Alternatively, you can bake the turkey on a rimmed baking sheet in a 375 to 400 degrees F oven for 90 minutes.)