This page sounds very credible, but I wish it would cite its sources. I guess I'll post the entire text of what it says:
Music by Nicholas Roubanis
English words by Fred Wise, Milton Leeds and S.K.Russell
Spanish words by J. Pina
Contrary to popular belief, Dick Dale did not write "Misirlou" (or "Miserlou," as it's also spelled). And it's not strictly a middle Eastern number, unless you stretch the definition to include southeastern Europe. "Misirlou" is, in fact, an Americanization of a traditional Greek song known as Ìéóéñëïý [unintelligible, even with a Greek font]. The dance that goes along with this song was also Americanized in "Zorba the Greek" and became the rage of parties for several years after the film's release (I can remember my parents going to a special party dedicated to mastering the dance).
"Misirlou" was published in sheet music form by Nicholas Roubanis in the mid-1930s. Roubanis was a musical scholar who published a book on the liturgy of the Greek Orthodox Church, but various sources also credit Milton Leeds, Fred Wise, Jose Rina, and others. It was a popular number for light classical pianists. Jan August had his first and biggest hit with the tune in the late 1940s, but it was also a hit for sweet band leader Wayne King.
Dick Dale adopted the tune as a virtuouso guitar piece when he began to perform for the southern California beach crowd in the late 1950s. Dale has said his guitar style was influenced by the music he heard played in Armenian families he grew up with. "Misirlou" was already well-established as an exotica standard by then, but either inspiration is credible.