Heat olive oil in a large sauce pan over medium heat. One hot, add the onion and cookfor 6-7 minutes or until softened. Add garlic, stir, and cook until fragrant, about 30 seconds. Stir in rice and cook until just starting to brown, about 3 minutes.
Add broth, tomato sauce, and tomatoes; bring to a boil. Add remaining ingredients (cilantro, oregano, and salt), stir, cover, and reduce heat to low. Cook rice for 15 minutes; turn off heat and allow to sit (covered) for about 10 minutes. Fluff with a fork and serve.