The quantum effects of gravity become apparent when particles of sufficiently small mass are located in the gravitational field of a large body of mass. In such conditions, the particles would experience the stepwise variation of the gravitational field as a series of rings in which the gravitational strength remains constant. Consequently, in such quantized gravitational fields, the orbital path of the particles would deviate from the circular path of the smooth classical gravity. In this article it is shown that under quantum effects of gravity, the path of an orbiting particle would look like a polygon with rounded vertices; like those of Saturn's hexagon. The side-count of such polygonal paths is shown to be a direct function of the width of the ring of constant gravity, which itself is a direct function of the mass of the orbiting particle. In the case of the polygonal paths of large side-count, each rounded vertex and its pair of immediate connecting edges, constitute a parabolic trajectory that the particle takes while traversing the width of the ring of constant gravity. The parabolic path of the particle is such that it gets tangent to the boundaries of the ring of constant gravity at two altitude extremes. In one extreme, when the path is tangent to the circle of high altitude, the particle velocity is less than what is required to maintain its altitude, hence, it descends afterward. In the other extreme, when the path is tangent to the circle of low altitude, the particle velocity is more than what is required to remain at that altitude, hence, it ascends afterward. This repeated altitude drops and gains results in the polygonal orbital path of the quantum gravity. The circular path of the classical mechanics emerges when the quantum effects of gravity is fully vanished by reducing the width of ring of constant gravity to zero, hence, increasing the polygon side-count unboundedly. In this limiting case, the circular path of the classical mechanics would be made of infinitesimal parabolas each fully tangent to the circular path at their vertices.