Sharyn McCrumb clearly states that the "song" is not authentic; "it was written for this book because I thought that I could not find a song so obscure that no reader would be familiar with it, so I composed one."
However, Sweetwater's Shelly Stevens penned a tune, and the song has been released as a cd single. Type "The Rowan Stave" in Google, and you can get ordering information. A reading from the book is also on the cd.