Actually, everything has a gravity pull of its own. Earth exerts its gravity on you, for example, but you also exert your own (minute) gravity on Earth.
Hmmm... it suddenly occurs to me that only things with mass exert gravity. So perhaps the question is still a valid one. If it isn't organic or artificial and doesn't exert its own gravity, it might be an energy being of some kind.
"Let mental culture go on advancing, let the natural sciences progress in even greater extent and depth, and the human mind widen itself as much as it desires: beyond the elevation and moral culture of Christianity, as it shines forth in the Gospels, it will not go." Goethe