EDIT: I checked a few of my clothing articles. The ones that I found that contain rayon did not state to dry clean, but simply hand wash in cold water and hang/line dry. I have a dress that does not contain rayon, but it states to dry clean only. I've never dry cleaned it, and just washed it in the washing machine and let it air dry. It has not shrunk or been damaged. I think you are safe to wash it.
It may not harm it, but it could potentially cause it to shrink. I have an old button-up shirt that is made of rayon (do not recall the percentage at this moment) that shrunk after washing it, but I have many other tank tops/articles that also included other materials, like spandex, that have not shrunk when washed. If it was quite expensive, you might want to get it dry cleaned, but otherwise I would personally just wash it in the washing machine at the "hand wash" cycle and let it air dry (laying flat would probably be best so as to not have the shape of the dress change due to being stretched out from the spandex). I'll go check out some of my articles of clothing to see if any state "dry clean only" on them.
