Preheat the oven to 350 degrees F (175 degrees C).
Brown sausage in a skillet over medium-high heat; drain grease. Add rice, onion, garlic, and peppers; cook and stir for 5 minutes. Stir in tomatoes, chicken broth, salt, pepper, and cayenne pepper. Transfer into a 9x13-inch baking dish.
Bake in the preheated oven until rice is tender and most of the liquid is absorbed, about 1 hour.