The strong Charge-Parity (CP) problem arises from the extreme smallness of the effective quantum chromodynamics (QCD) topological angle θ. This work demonstrates that θ vanishes identically in a class of Type IIB string compactifications with fixed-point moduli stabilization. The cancellation emerges as a structural consequence of flux quantization, supersymmetric extremization, and modular holomorphy, without invoking Peccei-Quinn symmetries, parameter tuning, or vacuum scanning. All contributions to θ are shown to be fixed by the same flux configuration that stabilizes the Kähler modulus at τ⋆ ≃ 220, previously derived from vacuum energy considerations. The axion vacuum expectation value, flux-induced gauge phase, and Yukawa determinant phase are individually derived and cancel exactly. The result establishes the strong CP problem as resolved by internal consistency of the fixed-point vacuum.