Assume a non uniform sphere, on a smooth horizontal floor it center of mass isn't at its geometrical center but on the line passing through geometrical center and parralel to horizontal floor.

My textbook claims it will move with horizontal acceleration and rotate with angular acceleration. I have no doubt about angular acceleration as there is net torque in some direction.

But what about horizontal acceleration both gravitational and normal force are opposite and in vertical direction. How will the horizontal acceleration produced?