No, you should not iron a leather jacket. Leather is not designed to be ironed, and the high heat from the iron can damage the leather, causing it to crack, shrink, or lose its shape. If your leather jacket is wrinkled, you can try hanging it in a steamy bathroom or using a garment steamer to gently remove the wrinkles. If the jacket is heavily creased or has deep-set wrinkles, it may be best to take it to a professional leather cleaner who can safely remove the wrinkles without damaging the genuine leather jacket.