This work investigates the quantization of angular momentum in galactic systems under the framework of Quaternion Angular-Momentum Gravity (QAMG). We show that the coupling between asymmetric angular-momentum fields and global neutrality conditions naturally produces discrete, quantized levels of total angular momentum for rotating self-organized gravitational systems. A macro-Planck constant, emerging from the long-range behavior of the gravitational field, is derived and shown to be consistent in order of magnitude with values extracted from SPARC rotation-curve data. The radialization of the dynamical equation yields a Bessel-type structure that constrains the allowed rotational states, providing a physical basis for discrete orbital levels similar to quantum bound states. Numerical examples and observational implications are presented, demonstrating that angular-momentum quantization may offer a unified description of galactic rotation anomalies, self-organization, and large-scale gravitational coherence.