Found on page 3 of Games and Dances: A Selected Collection of Games, Song-games and Dances Suitable for Schools, Playgrounds, Gymnastic Associations, Boys' & Girls' Clubs, Etc By William Albin Stecher · 1916
In the preface the author thanks the Milton Bradley company for permission to use the song, but I'm not sure
I found two sources that says there's a recording on Victor Records #17568. I found it on Ebay, but it was only the sleeve.