Cook the pasta according to the package directions, reserving ¾ cup of the cooking water; drain the pasta and return it to the pot.
Meanwhile, heat the oil in a large skillet over medium-high heat. Add the andouille and brown, tossing occasionally, 3 to 5 minutes. Transfer to a plate; reserve the skillet.
Add the tomatoes, bell pepper, onion, oregano, ½ teaspoon salt, and ¼ teaspoon black pepper to the drippings in the skillet and cook, tossing occasionally, until the tomatoes burst, 6 to 8 minutes. Remove the oregano sprigs.
Add the andouille, vegetables, and ½ cup of the cooking water to the pasta. Cook over medium heat, tossing, until the liquid is slightly thickened and coats the pasta, 1 to 2 minutes (adding more cooking water as needed to loosen the sauce). Sprinkle with the oregano leaves.