Green’s Dictionary of Slang

(orig. US) to go out looking for female conquests.

1926		Odum & Johnson Negro Workaday Songs 32: [song title] If You Sheik on Your Mama.
1928		R. Fisher Walls Of Jericho 148: Thought he might need some help if he was out sheikin’.
1929		Helen Kane ‘He’s So Unusual’ 🎵 Hooh! What that boy knows! / He’s up in his Latin and Greek, / But in his sheikin’, he’s weak!
1931		Worker (Brisbane) 28 Oct. 19: They sheik their sheilas in the sheds / And shear sheep in the city.
1934		(con. 1920s) J.T. Farrell Young Manhood in Studs Lonigan (1936) 285: With all the sheiking you do, you still don’t know what it’s for.