This work introduces a quantum extension of Retarded Consistency Field Theory (RCFT), a framework in which the present is not assumed as a primitive instantaneous object but emerges through the resolution of delayed consistency across prior history. Instead of starting from local time evolution alone, the theory treats causal memory and history dependence as foundational and formulates quantum dynamics on a history space rather than on an instantaneous state space only. The paper develops a retarded consistency action, a history-weighted path integral, and a history-space Schrödinger formulation for non-Markovian quantum dynamics. In the short-delay limit, the framework reduces to ordinary local mechanics and standard quantum theory, while finite-delay effects generate controlled corrections governed by the moments of a causal memory kernel. The formalism also shows how inertial motion and geodesic structure can appear as local limits of the same delayed consistency principle. Conceptually, the theory proposes that quantum reality is organized not by a pre-given temporal present but by interference among possible histories weighted by delayed consistency. In this picture, the physically realized present is an emergent endpoint of constructive consistency selection. The work positions RCFT as a unified foundation for rethinking time, inertia, and gravitational structure within a quantum history-based framework.