Remove the giblets from the chicken cavity if present. Pat the entire chicken very dry with paper towels, including inside the cavity. Letting the chicken sit uncovered in the fridge for a few hours beforehand will also help the skin crisp up.
In a small bowl, combine the smoked paprika, garlic powder, onion powder, thyme, oregano, salt, and black pepper. Rub the olive oil all over the outside and inside of the chicken, then coat it generously and evenly with the seasoning mixture.
Stuff the cavity of the chicken with the lemon half and smashed garlic cloves. Tie the legs together loosely with kitchen twine if desired for even cooking.
Preheat the air fryer to 360°F for 3 minutes.
Place the chicken breast side down in the air fryer basket. Air fry for 30 minutes at 360°F.
Carefully flip the chicken so it is breast side up. Increase the temperature to 380°F and continue cooking for 20 to 25 minutes more, until the skin is deep golden brown and crispy and the internal temperature at the thickest part of the thigh reads 165°F.
Transfer the chicken to a cutting board and let it rest for at least 10 to 15 minutes before carving. This resting period is essential so the juices settle back into the meat for a moist, tender result.