You could left "lui" but not si. Girare is a reflective verb. It should be translated as "he turns himself towards me". Si means "himself" in this context
Yours makes more sense. I completely guessed at what it meant, and got lucky. Do Native Italians actually say crap like this? Isn't there a more reasonable way to say this?
Actually, the literal interpretation should be "He turns himself towards me". "Girare" requires a direct object, and if there isn't one, then it's a reflexive pronoun for the subject.