Cook the pasta according to the package directions, reserving ¾ cup of the cooking water; drain the pasta and return it to the pot.
Meanwhile, heat the oil in a large skillet over medium-high heat.
Add the shrimp, garlic, and ½ teaspoon each salt and pepper and cook, tossing occasionally, until the shrimp are opaque throughout, 2 to 3 minutes. Add the shrimp and ½ cup of the cooking water to the pasta. Cook over medium heat, tossing, until the liquid is slightly thickened and coats the pasta, 1 to 2 minutes (adding more cooking water as needed to loosen the sauce).
Fold the arugula and pepperoncini into the pasta and sprinkle with the Feta.