Yes, there is a song for this film, it's quite funny, and both Stephen Horne of the UK and I have performed it at film festivals, mine at the San Francisco Silent Film Festival a couple of years ago. Here's the first verse and chorus. It's a jaunty tune in 6/8.
The rajah's he's come from ranjipoo only to stay a month or two and you can bet the raja knows what's what you couldn't lose him in regent Street at any old game he's hard to beat the sort of sport who's always On the spot in his own native land he's so precise in everything but Over here he has his fling
Oh all the girls admire the rollicking rajah the wonderful rajah he's a Multimillionaire each day in rotten row he's riding a charger and the Rajah looks all there he wears a bunch of diamonds stuck in his turban In front of his turban and rubies too all the girls salaam the great Ram jam the rollicking rajah of ranjipoo
I plan to record it and put it online before the end of the year (2015). Stay tuned. Send me an email and I'll let you know. Donald Sosin