Heat a large nonstick skillet over medium-high. Add sausage; cook, stirring occasionally, until browned, about 4 minutes. Transfer to a 5- to 6-quart slow cooker. Add stock, tomatoes and chiles, onion, bell pepper, celery, tomato paste, Creole seasoning, garlic, and salt. Cover and cook on low 4 hours.
Stir in rice. Cover and cook on low until rice is tender, about 2 hours.
Stir in shrimp. Cover and cook on low 8 minutes. Divide soup evenly among 6 bowls. Sprinkle with parsley.