Preheat the oven to 350 degrees F (175 degrees C).
Bring a large pot of lightly salted water to a boil; cook the rotini at a boil until tender yet firm to the bite, about 10 minutes; drain.
Heat olive oil in a large skillet over medium-high heat. Add ground turkey and break it up with a wooden spoon. Add chili powder, garlic, cumin, cayenne pepper, oregano, and black pepper; mix thoroughly. Cook and stir until turkey is browned and crumbly, 5 to 7 minutes. Add corn, diced tomatoes and chiles, green bell pepper, onion, celery, and carrot; mix thoroughly.
Place lid on skillet. Cook until vegetables are tender, stirring occasionally, about 8 minutes. Add tomato sauce; let simmer until thickened, about 5 minutes. Transfer turkey mixture to a 9x13-inch casserole dish and add the cooked pasta. Mix everything together. Top with pepper Jack cheese.
Bake in the preheated oven until cheese is melted, about 10 minutes.