Heat 1 tablespoon oil in a Dutch oven. Add sausage and cook until browned. Remove sausage with a slotted spoon and set aside.
Add remaining oil to the grease in the Dutch oven. Add onion, green pepper and celery and cook until soft, about 5 to 7 minutes, stirring occasionally.
Add garlic and cook 1 minute.
Add diced tomatoes, tomato sauce, chicken broth, Worcestershire sauce, Cajun seasoning, Tabasco sauce, pepper, and thyme.
Bring mixture to a simmer and stir in rice and reserved sausage. Cover and cook on low, stirring occasionally, for 20 to 25 minutes. I like to cook it uncovered for the last 5 minutes to help thicken it up.
Stir in turkey and serve.