Heat the oil in a large frying pan over medium hight heat. Add the sausage and brown on both sides - about 5 minutes total. Reduce heat to medium and add the onion. Cook, stirring occasionally, for 5 minutes.
Drain off the grease. Add the broth and rice and bring to a boil. Reduce heat, cover, and simmer for 15 minutes.
Stir in the shrimp, cover, and cook for an additional 5 minutes. Remove from heat.