The Standard Model of particle physics relies on the point-particle hypothesis, which inherentlyleads to renormalization divergences and fails to derive the elementary charge e from first principles. In this article, we propose a non-perturbative geometric unification model where the electron is reconstructed as a toroidal photon soliton confined within a Kerr-Newman vacuum background. By unifying Einstein-Cartan gravity with Born-Infeld electrodynamics, we demonstrate that the stability of such solitons arises from the dynamical equilibrium between torsion-induced gravitational attraction and non-linear electromagnetic repulsion at the Schwinger limit. We rigorously derive theelementary charge as a topological winding number, corrected by a metric coupling factor χ ≈ 1.092 which arises from the frame-dragging effect of the rotating vacuum. This geometric correction successfully resolves the long-standing 8.5% discrepancy in the semi-classical Williamson-van der Mark model. Furthermore, we discuss the phenomenological consistency of this extended structure with high-energy scattering experiments via Bjorken scaling. The model suggests that the Higgs field is the order parameter of a torsion condensate, providing a unified geometric origin for mass, charge, and the cosmological constant.