Heat the olive oil in a large skillet over medium heat.
Remove the sausage from its casing and crumble it into the skillet. Cook until browned, about 5-7 minutes, breaking it apart as it cooks.
Add the diced onion, green bell pepper, and celery to the skillet. Sauté until the vegetables soften, about 5 minutes.
Stir in the minced garlic and continue cooking for another minute until fragrant.
Sprinkle the Cajun seasoning, salt, black pepper, and cayenne pepper over the mixture. Stir well to combine.
Add the rice to the skillet and stir to coat it in the sausage and vegetable mixture.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, reduce the heat to low, cover, and simmer for about 20 minutes or until the rice is cooked and has absorbed the liquid.
Fluff the rice with a fork and taste for seasoning, adjusting as necessary.
Serve the dirty rice hot, garnished with sliced green onions and chopped parsley.