Susan from the Rotary Heritage committee passed along this message:
 
The tradition of singing at Rotary club meetings began in 1905 with Rotarian Harry L. Ruggles of the Rotary Club of Chicago. New Rotary clubs formed, and the practice of singing at club meetings caught on. RI doesn’t track which clubs sing so I don’t have a history of singing clubs. You might try the International Fellowship of Rotarian Musicians, https://ifrm.org.
 
You might be interested in these mentions of singing in past issues of The Rotarian:
  • July 1957, pages 14-16, To Sing or Not to Sing?
  • November 1966, page 39, Everybody…Sing!
  • February 1994, pages 12 & 66, Letter to the Editor: Sing, Rotarians, Sing!
They can be viewed online at https://books.google.com/books?id=vzQEAAAAMBAJ&dq=rotarian&source=gbs_all_issues; regrettably, Google doesn’t make is possible print or download.
 
Ruggles's company published an unofficial Book of Songs -- a collection of patriotic tunes, familiar standards, and Rotary songs (many penned by Rotarians) -- to help clubs make singing a regular part of their meetings. The first official edition of Ruggles's songbook, Songs for the Rotary Club , was published in 1918 and provided lyrics only. Editions with musical notation appeared in 1925.
 
Later editions offered advice on incorporating music into Rotary club meetings. The 1933 edition encouraged Rotarians to add singing to their weekly meeting agendas. The 1935 edition advised clubs to sing prior to lunch and to select a song leader on the basis of personality, not musical talent.  The current edition of the songbook is available at https://shop.rotary.org/songs-for-the-rotary-club-words-and-music-003.