Remove the silver membrane from the back of the ribs by sliding a knife under it at one end, gripping it with a paper towel, and peeling it off in a steady pull.
Pat the ribs dry, then combine smoked paprika, garlic powder, onion powder, brown sugar, kosher salt, black pepper, chili powder, oregano, and cayenne in a small bowl. Drizzle ribs with olive oil, then generously apply the dry rub to all sides, pressing it in firmly.
Cut the rack in half if needed to fit your air fryer. Place each piece on a large sheet of heavy-duty foil, add 1 tablespoon of water per packet, and wrap tightly, crimping the edges firmly to create a sealed packet.
Preheat air fryer to 380°F (193°C) for 3-5 minutes. Pour 2 tablespoons of water into the bottom of the air fryer drawer or drip tray to prevent smoking.
Place the foil-wrapped rib packets in the air fryer basket in a single layer, bone-side down. Air fry at 380°F (193°C) for 25 minutes without opening the basket.
Carefully remove foil packets, open them to release steam, and check internal temperature. It should read between 185-195°F (85-90°C). Brush generously with BBQ sauce.
Place unwrapped, sauced ribs back in the air fryer basket, bone-side down. Air fry at 380°F (193°C) for 8-10 minutes until the sauce caramelizes and the internal temperature reaches 190-195°F (88-90°C).
Remove ribs from air fryer and let them rest on a cutting board for 5 minutes. Cut between the bones to separate individual ribs and serve with additional BBQ sauce on the side.