Preheat the air fryer to 375°F (190°C).
In a mixing bowl, combine shredded chicken, mozzarella cheese, garlic powder, and sauce until evenly incorporated.
Divide the mixture into four equal portions.
Place one portion of the mixture in the center of each tortilla.
Fold the left and right sides of the tortilla toward the center, then roll tightly from the bottom to form a sealed wrap.
Lightly brush the entire exterior of each wrap with olive oil to facilitate browning.
Place the wraps seam-side down in the air fryer basket in a single layer.
Air fry for 8 to 10 minutes, flipping once at the 5-minute mark, until the exterior is golden brown and crispy.
Remove from the air fryer and allow to rest for 2 minutes before slicing diagonally.