Heat peanut oil in a skillet over medium heat. Season andouille sausage with Cajun seasoning; cook in hot oil until browned, about 5 minutes. Drain excess grease from the skillet. Set sausage aside.
Heat vegetable broth in a saucepan over medium heat until warm; add sweet potato and bring to boil. Cook until potato is tender, about 10 minutes. Stir sausage and corn into the broth with the sweet potato. Bring the mixture to a boil and serve immediately.