If the electromagnetic four-potential is a physical field rather than a gauge class, its irrotational component is physical as well, and the geometry of spacetime can respond to it directly. We develop the consequences of this reading in the context of Einstein-Cartan gravity at the classical level. Imposing metric compatibility and linear dependence of the affine connection on the potential, we derive a unique one-parameter extension of the Levi-Civita connection. The resulting torsion is purely axial, and its Ricci scalar contributes a term $+6lambda^2 A_mu A^mu$ that generates Proca electrodynamics with photon mass $m_gamma = sqrt{3/(4pi)},lambda M_{m Pl}$, where $lambda$ is a dimensionless coupling. The same coupling also produces a universal spin-dependent force on matter and an axial-vector coupling to fermions. Because a single parameter controls all four observable sectors, the four sectors are correlated by construction, and the correlation is a signature of the geometric mechanism. We verify that the construction does not generate parity violation in the vacuum propagation of photons, and we confront the framework with laboratory, astrophysical, and cosmological bounds. The solar-wind bound on the photon mass forces $lambda lesssim 2 times 10^{-46}$, which replaces the unexplained smallness of the photon mass by an unexplained smallness of the geometric coupling. We emphasize that the paper is a classical study; the quantization of the theory and its consequences for unitarity and for the cosmological abundance of longitudinal modes are left open. Three appendices contain the detailed derivations of the uniqueness of the connection, the Ricci scalar computation, and the spin-torsion force.