Of course, you don't have to go back that far.  Many collected editions of Burns include the (written) music for his songs; Burns: Poems and Songs (Oxford University Press) ought to be easy enough to find.  You may have more difficulty finding recorded versions, however; the entry in  The Burns Encyclopaedia for  Jean Jaffray (about whom the song was written) mentions that the air, by Robert Riddell, "spans two octaves, and is very nearly unsingable".  The text is available online, here:  I Gaed A Waefu' Gate Yestreen.

Malcolm