Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces to the skillet and cook until browned on all sides, about 5-6 minutes. Remove the chicken and set aside.
Add the sliced smoked turkey sausage to the same skillet and cook until browned, about 3-4 minutes. Remove and set aside with the chicken.
Reduce heat to medium. Add the diced onion, green bell pepper, and celery to the skillet. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the diced tomatoes with their juice, chicken broth, Cajun seasoning, smoked paprika, thyme, oregano, cayenne pepper, salt, and black pepper.
Return the browned chicken and sausage to the skillet and bring the mixture to a boil.
Add the uncooked penne pasta to the skillet, stirring to combine.
Reduce heat to medium-low, cover, and simmer for 15-18 minutes, stirring occasionally, until the pasta is tender and the sauce has thickened.
Taste and adjust seasoning with additional salt and pepper if needed.
Remove from heat and let stand, covered, for 5 minutes before serving.
Garnish with sliced green onions and chopped fresh parsley before serving.