Preheat oven to 375 degrees F (190 degrees C). Grease a baking sheet with cooking spray.
Mix artichoke hearts, sour cream, cream cheese, spinach, and garlic powder in a bowl.
Unroll breadstick dough, separate into breadsticks, and cut in half. Roll up breadstick dough tightly into spirals or pinwheels and arrange on the prepared baking sheet. Place about 1 tablespoon of artichoke mixture on each pinwheel and top with Parmesan cheese.
Bake in the preheated oven until golden brown and puffed, 10 to 15 minutes.