This site calls it a Burns Original, but I think it's safe to assume that it's Burns' reworking of a traditional theme or song.

Jim Malcolm, who should know, has recorded it on his CD "Acquaintance - JM sings songs of Robert Burns".

The ultimate Burns site, www.robertburns.org, appears to be down at the moment, but I think you can safel attribute the song to Rabbie.

By the way, I specialise in CD graphics (am working on the new Mudcat CD series at the moment). PM me if you're interested.