Place split chicken wings into a mixing bowl. Sprinkle with salt, black pepper, and cayenne pepper. Toss to evenly coat pieces. Cover with plastic wrap and refrigerate for at least 2 hours or overnight.
Place rice flour in a shallow dish. Dredge chicken wing pieces in small batches in the flour and transfer to a plate. Arrange pieces so there is some space between them; allow wings to sit out for 15 minutes before frying.
Line a baking sheet with paper towels; place a draining rack on the towels.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C). Transfer wings to oil; fry until inside is crispy and golden brown and chicken is cooked through, 10 to 12 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
Remove wings from oil with a slotted spoon and drain on a rack placed over paper towels.