The same sheer and semi-sheer appearance of the rayon that makes it attractive can also make it difficult to iron. Not all rayon garments are the same. Rayon can vary according to the finish, construction and dyes that have been applied to it. You should always defer to the manufacturer instructions on caring for your clothing; however, there are some basic steps that generally work on removing wrinkles from rayon fabrics.
Set your iron to the correct setting. Depending on the options available on your appliance, this will be the lowest available setting or, if offered, the synthetic setting without steam.
Turn your garment inside out.
Mist the item slightly with a spray bottle containing water. The goal is to make the garment damp, not wet.
Iron your garment quickly, using the least amount of time needed to remove wrinkles. Keep the iron constantly moving, never lingering in a single spot for too long. Avoid ironing a single spot for more than two to three seconds.
Allow the garment to cool by placing it on a hanger.