Bring a large pot of heavily salted water to a boil. Cook the rigatoni pasta according to the package directions until al dente, then drain it in a colander.
In a mixing bowl, toss the cooked pasta with olive oil, Parmesan cheese, Italian seasoning, garlic powder, and a generous pinch of salt and black pepper until well coated.
Preheat the air fryer to 400°F, then add the seasoned pasta and air fry for 12–15 minutes, shaking the basket a couple of times to ensure even cooking.
To make the feta dip, combine the crumbled feta, Greek yogurt, and garlic in a food processor. Pulse until you achieve small crumbs, then stream in the olive oil while processing until the mixture is creamy, about 4–5 minutes.
Serve the crispy pasta chips warm alongside the whipped feta dip for dipping.