We extend the Holographic Photon Continuity framework into Riemann-Cartan geometry(U4) to analyze the dynamical interaction between extra-dimensional topological currentsand gravitational torsion. Standard general relativity assumes a torsion-free Levi-Civitaconnection; however, coupling the bulk Higgs-photon sheaf to a non-symmetric affine connection fundamentally alters the spectral geometry of the system. We demonstrate thatmapping the holographic boundary coupling to a Riemann-Cartan background naturallyleads to an APS-type index formulation including torsion-dependent corrections, allowingthe Nieh-Yan invariant together with torsion-dependent characteristic classes to contributeto the bulk obstruction class.Consequently, the Holographic Photon Law (Lholo), which protects the integrity of the4D Bianchi identity (dF = 0), becomes strictly torsion-dependent. This implies that macroscopic gravitational torsion acts as a direct catalyst for anomaly inflow, dynamically shiftingthe quantized index charge (Qindex) flowing from the extra dimensions. This formulationpredicts profound cosmological and astrophysical signatures: photons traversing torsionrich environments—such as primordial defect backgrounds or the vicinities of ultra-densefermionic spin matter—must exhibit anomalous phase shifts and topological vacuum birefringence. Ultimately, this framework establishes a mathematically consistent, testable bridgebetween Einstein-Cartan gravity, derived category topology, and observable quantum optics, providing a microscopic derivation, proving interpretation uniqueness, and identifyingtestable observables.