Preheat your oven to 425°F (220°C) and line a large baking sheet with parchment paper or a lightly oiled rack.
Pat the drumsticks dry with paper towels. This helps the Cajun spice stick and the skin crisp up nicely.
In a small bowl, whisk together paprika, garlic powder, onion powder, cumin, oregano, red pepper flakes, salt, and black pepper.
Toss the drumsticks in a bowl with olive oil until they’re evenly coated. Sprinkle the spice mix over the drumsticks and rub it in with your hands so every piece has a good coat.
Arrange the drumsticks on the prepared sheet in a single layer. If you have a rack, place the drumsticks on the rack; this helps air circulate and makes the skin even crisper.
Bake for about 30 to 35 minutes, turning once halfway through, until the internal temperature reaches 165°F (74°C) and the skin is crisp and deeply colored.
If you want extra color and crunch, switch to broil for the last 1–2 minutes, watching closely to prevent burning.
Let the drumsticks rest for 5 minutes before serving. A squeeze of lemon or a quick herb sprinkle (parsley or chives) brightens the flavors.