Place a large pot over medium heat and add the sliced Andouille sausage. Cook for 5 to 6 minutes, stirring occasionally, until the edges brown and some fat renders out.
Add the diced onion, bell peppers, and celery to the pot. Cook for 4 to 5 minutes until the vegetables soften slightly.
Stir in the minced garlic, smoked paprika, cayenne pepper, dried thyme, salt, and black pepper. Cook for 1 minute until the garlic becomes fragrant.
Add the rice and stir to coat it with the spices and sausage drippings.
Pour in the diced tomatoes with their juices and the chicken broth. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 20 minutes until the rice is tender and the liquid is absorbed.
Remove the pot from the heat and let it sit covered for 5 minutes. Fluff the rice with a fork and top with the sliced green onions before serving.