Preheat an outdoor grill to high heat, between 400 and 450°F.
In a small bowl, whisk together the olive oil, smoked paprika, garlic powder, kosher salt, black pepper, and cayenne pepper until combined.
Place the okra pods in a large bowl. Pour the spice blend over the okra and toss well to coat evenly.
Thread the okra pods onto skewers, leaving a little space between each pod for even grilling. If using wooden skewers, soak them in water for 30 minutes before using.
Place the okra on the preheated grill over direct heat. Grill for about 5 minutes until bright green with visible grill marks. Turn and grill the other side for an additional 5 minutes until grill marks are visible on the second side as well. Remove from the grill and serve immediately.