Where can I find sheet music for the theme song?

'Course there is. You still need notations for the different vocal parts, and of course the actual melody of the song. One guy sings the "ooh-ah, doo-bay ooh-wah" in the background, while someone else sings the main lyrics, the whole ensemble sings "Where in the world is --" and the deep-voiced guy sings "CARMEN SANDIEGO?"

I googled it and managed to find a really old Usenet newsgroup discussion archived from way back in 1994, which directs the person to contact a certain Deke Sharon, who apparently does a capella arrangements at some conservatory:

https://groups.google.com/forum/#!topic/rec.music.a-cappella/pdt6ENzJAew

The copyright is apparently owned by Warner Music, who is notoriously difficult to get performance rights from (this was the infamous "Happy Birthday" rights holder, who ended up losing their landmark case involving arguably the most well-known ditty in modern history in court). But, OP might have some luck scouting around for that other person mentioned in the Usenet posting, if he's still active -- or even still alive...