The fine structure constant α occupies a singular position in fundamental physics. As a dimensionless parameter governing electromagnetic interactions, its numerical value appears accidental within the Standard Model: it is neither fixed by symmetry, nor by renormalization group flow, nor by known dynamical mechanisms. In Topological Fixed Point Theory (TFPT), we argue that this apparent arbitrariness is an illusion. TFPT proposes that α is not a free input parameter but the unique positive fixed point of a quantum effective potential, enforced by global topological and geometric consistency. The theory is built from a minimal axiomatic kernel rooted entirely in established frameworks: Riemann–Cartan geometry with torsion, anomaly-induced Chern–Simons terms, background-field gauge consistency, and spectral index theory. At no stage are continuous fit parameters, scans, or anthropic assumptions introduced. The construction rests on two universal, dimensionless invariants that are computed rather than postulated. The first is the topological coupling c₃ = 1/(8π), fixed by Chern–Simons quantization in eleven-dimensional theory. The second is a geometric scale φ₀ = 1/(6π) + 3/(256π⁴), derived from a Möbius-type reduction on the orientable double cover of a non-orientable base manifold. Its normalization is fixed by Atiyah–Patodi–Singer η-invariant gluing and a discrete spin-lifted deficit. Both invariants are determined entirely by global geometry and topology. When combined with the Standard Model abelian trace b₁ = 41/10, interpreted not as a running beta-function coefficient but as a spectral boundary index, these inputs yield a cubic fixed-point equation for the electromagnetic coupling. The equation admits exactly one physically admissible solution. Incorporating the geometrically required backreaction on the orientable double cover (k = 2) and the derived two-defect partition fixed by SU(5) holonomy degeneracy (g = 5), the self-consistent solution yields α⁻¹ = 137.035999216…, in agreement with the CODATA 2022 value at the sub-ppm level, without tuning or adjustment. Crucially, the same kernel fixes additional observables. The axion–photon coupling is uniquely predicted as gₐγγ = −4c₃, and a quantized minimal topological axion excursion yields a definite prediction for cosmic birefringence, β ≈ 0.242°, consistent with current CMB polarization measurements within reported uncertainties. Independent two-loop renormalization-group evolution further reveals percent-level fingerprints of the same invariants in the high-energy behavior of the strong coupling. TFPT is explicitly falsifiable. Any future measurement of α deviating beyond the ppm level, a birefringence angle outside the predicted window, or incompatible high-energy RG fingerprints would rule out the framework. At the same time, the theory makes no claim to explain all of particle physics and does not rely on speculative landscapes, adjustable extra dimensions, or hidden sectors beyond a minimal axion extension. In this sense, Topological Fixed Point Theory reframes the fine structure constant not as a numerical coincidence, but as a necessary consequence of global topology, geometry, and quantum consistency. The value of α is not selected. It is enforced.