If you use Google Book Search to search for the opening line of that song, you'll find it in several old anthologies, the oldest of which is The Modern Scottish Minstrel, edited by Charles Rogers, Edinburgh, 1857.
THE ARABY MAID is on page 160. The words are nearly identical to what is posted above.
It is attributed to Rev. Thomas Gordon Torry Anderson (1805-1856) whose biography begins on page 158. It says he wrote THE ARABY MAID in 1833.