Bring a large pot of water to a boil. Boil sausage until hot, 8 to 12 minutes; drain.
Heat canola oil in a pot over medium-high heat; saute sausage, celery, bell pepper, and onion in hot oil until vegetables start to soften, about 5 minutes.
Stir chicken and Cajun seasoning into the vegetable mixture. Pour broth and tomatoes into the pot; bring to a boil, add the rice, and stir. Return mixture to a boil, reduce heat to medium-low, cover pot, and simmer mixture until for 5 minutes. Remove cover, stir, and continue to simmer until the rice has absorbed the liquid and is tender, about 5 minutes more.