You're right, Backstage Manager: "Ahab the Arab" was written and first recorded by Ray Stevens. It was a top-10 hit in 1962. There is a copy of the lyrics on his web site.

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Lyrics below transcribed from The Lester S. Levy Collection of Sheet Music:

SHEIK OF ARABY
Words, Harry B. Smith & Francis Wheeler. Music, Ted Snyder. 1921.

1. Over the desert wild and free
Rides the bold sheik of Araby.
His Arab band at his command
Follows his love's caravan.
Under the shadow of the palms
He sings to call her to his arms:

CHORUS: I'm the Sheik of Araby.
Your love belongs to me.
At night when you're asleep,
Into your tent I'll creep.
The stars that shine above
Will light our way to love.
You'll rule this land with me,
The Sheik of Araby.

2. While stars are fading in the dawn,
Over the desert they'll be gone.
His captured bride close by his side,
Swift as the wind they will ride.
Proudly he scorns her smile or tear.
Soon he will conquer love by fear. CHORUS

[AMG - All Music Guide lists about 500 recordings of this song. Some notable ones are The Beatles, Sidney Bechet, Milton Brown, Eddie Condon, Tommy Dorsey, Duke Ellington, Benny Goodman, Coleman Hawkins, Woody Herman, Harry James, Spike Jones, Leon Redbone, Django Reinhardt, Art Tatum, Jack Teagarden, and Fats Waller.

[Lyrics sung by Jim Kweskin with Maria Muldaur are posted here.

[The song was inspired by the 1921 silent film "The Sheik" starring Rudolph Valentino.]