Stir the shredded chicken together with the ranch dressing until every piece is lightly coated. Season with salt and pepper, then taste — rotisserie chicken comes pre-salted, so you'll need less than you think.
Stack the tortillas on a plate, cover with a damp paper towel, and microwave 20 seconds. Cold tortillas split at the fold; warm ones roll tight and stay closed.
Lay the tortillas flat. Divide the chicken between them, keeping it in a line down the center rather than spread to the edges. Top with cheese, then lettuce and tomato. Fold the sides in, then roll up tightly from the bottom, burrito-style.
Preheat the air fryer to 380°F (193°C). Don't skip this — a cold basket means the tortilla dries out before it browns.
Brush or spray the outside of each wrap with oil. Place them seam-side down with space between them so air can circulate on all sides. Cook 8–10 minutes, flipping halfway, until deep golden and crackly.
Let the wraps rest two minutes. The cheese is molten and the filling needs a moment to set, or it slides out the end when you slice. Cut on the diagonal and serve.