Yes, most cooking oils are naturally gluten-free.
Examples of gluten-free oils include canola oil, sunflower oil, olive oil and vegetable oil. However, any oil could potentially come into contact with gluten during manufacturing processes, therefore we always recommend reading labels and trusting certified gluten-free products, especially if they include additives or flavorings. Reach out to manufacturers if you have any questions.
While oil itself is generally gluten-free, when ordering items that are fried in oils at restaurants, be sure to ask if the kitchen uses a dedicated fryer for gluten-free items, as some foods cooked in oil may not be gluten-free (such as breaded meats) and therefore would cause issues with cross-contact.