Rayon is a man-made fiber that is very durable and can make lovely, light formal wear. One problem with synthetic fibers is that some are prone to wrinkles, but the wrinkles are difficult to remove since the fibers melt at higher temperatures. Some cleaners will attempt to remove wrinkles from rayon by using a low-temperature steam iron, but you can also work on the problem at home.
Arrange the dress on a plastic or padded hanger. Be sure that the dress is hanging straight with no tucks or creases.
Hang the dress on the back of the door or on the wall of your bathroom. You can hang it in the shower if you're able to place it out of range of any spray from the shower. No water should fall on the dress.
Turn the shower on and let your bathroom fill with steam, if you're in a hurry. Otherwise, leave the dress for several days and allow the steam and moisture from normal activity to erase the wrinkles in the dress.
Remove the dress from the bathroom and hang it in an open, airy location until any residual dampness is gone. You can now wear the wrinkle-free dress.
You can also try ironing the dress on the wrong side with a steam iron set at low temperature. Use a cotton pressing cloth between the iron and the fabric.
Don't apply a hot iron directly to the fabric or put the dress in a hot dryer.