Combine the tomato sauce, oil, mustard, thyme, oregano, Cajun seasoning and black pepper in a large bowl. Add the drumsticks and mix well to coat evenly with the tomato sauce mixture. Cover and refrigerate for 30 minutes.
Preheat the oven to 180°C.
Place the chicken drumsticks in an oven dish lined with baking paper. Bake for 30 minutes or until the juices run clear when the thickest part of the drumstick is pierced with a skewer.