The person that wrote the words to this song was very poor at spelling. "Old MacDonald had a farm, E.I.E.I.O." E.I.E.I.O.? It should be F.A.R.M.
Despite the Scottish protagonist, "McDonald's Farm" appears to be a truly American folksong. The earliest records of it don't go back more than a century and come from our own hill country, Appalachia. One early version of the song was "Old McDonald Had a Mule." The "EIEIO" may have been merely an attempt to spell the sound of the mule's bray, which we have now standardized as "hee-haw."