Preheat an air fryer to 360 degrees F (180 degrees C) according to manufacturer's instructions.

Stir kale leaves off the stems and chop into small pieces. Place in a large bowl; add olive oil, salt, paprika, garlic powder, pepper, and cayenne. Toss until well coated.

Add a layer of kale leaves to the air fryer basket. Cook for 3 minutes. Shake the basket and pour kale out onto a cutting board or baking sheet to cool and crisp up. Repeat with remaining kale, working in batches to prevent it from steaming and getting soggy.