We investigated the upper critical field of a large single grain of the Nb-substituted van der Waals layered quasicrystal (Ta_(0.7)Nb_(0.3))_(1.6)Te. The sample exhibits a sharp superconducting transition at T_c = 1.35 K, the highest value reported to date among quasicrystal superconductors. The angular dependence of the critical field exhibits a pronounced criterion dependence: the field determined using the 10% R_N (R_N: normal-state resistance) criterion is well described by the anisotropic Ginzburg-Landau model, whereas those determined using the 65% and 90% R_N criteria exhibit Tinkham-like angular dependence characteristic of two-dimensional superconductivity. The high-field part of the resistive transition is well described by a surface-superconductivity model and exhibits a pronounced excitation-current dependence for magnetic fields close to the ab plane, supporting the presence of surface superconductivity on the quasiperiodic ab-plane surfaces. The bulk H_c2 is strongly anisotropic, with the in-plane H_c2 exceeding the weak-coupling Pauli limit by a factor of approximately 2.5. For both field orientations, H_c2(T) deviates upward from the conventional dirty-limit Werthamer-Helfand-Hohenberg prediction at low temperatures. A phenomenologically modified Ginzburg-Landau-Abrikosov-Gorkov model incorporating a spatial distribution of the electronic diffusivity substantially improves the description of H_c2(T), suggesting that spatial variations in electronic transport properties may contribute to its anomalous temperature dependence.