Cut the tuna into 16 evenly sized chunks and place in a shallow bowl with the olive oil, garlic and chopped rosemary; season with salt and pepper. Toss to combine. Cover and let stand at room temperature, tossing occasionally, for 30 minutes.
Preheat a grill or grill pan to medium-high. Skewer the tuna chunks onto the rosemary sprigs, about 1/2 inch apart. Place the skewered tuna on the grill and drizzle with the remaining marinade. Grill, turning with tongs, until cooked on all sides, about 4 minutes for medium-rare.