Preheat an outdoor grill for medium heat and lightly oil the grate.

Scrub sweet potatoes thoroughly under cold running water. Cut each potato lengthwise into 8 wedges. Place wedges in a bowl and toss with 2 tablespoons of oil. Combine remaining olive oil, paprika, salt, garlic powder, cinnamon, and cayenne in a separate small bowl.

Place wedges on the grill perpendicular to the grates and reduce heat to low. Grill over low heat, turning occasionally, until potatoes are soft, 16 to 18 minutes. Brush wedges with oil mixture on both sides, and grill 1 to 2 minutes more, then transfer to a plate.