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High-frequency expressions for the field scattered by a half-plane with a perfectly conducting and an anisotropic impedance face are provided in the format of the uniform geometrical theory of diffraction (UTD), when the half-plane is illuminated by an arbitrarily polarized plane wave obliquely incident on its edge. The loaded face is characterized by a tensor surface impedance with principal anisotropy axes arbitrarily oriented with respect to the edge; a vanishing surface impedance is exhibited in one of the principal directions. This kind of tensor surface impedance can be suitably applied for analyzing the effects on the scattered field of corrugated surfaces or grounded dielectric slabs periodically loaded by metallic strips. This solution extends previous high-frequency formulations valid in those cases in which the direction of corrugations or strips is either parallel or perpendicular to the edge. The analysis is performed by resorting to the Sommerfeld-Maliuzhinets method. To determine the spectral solution, a special function is needed that differs from the standard Maliuzhinets one and was originally introduced to study the electromagnetic scattering by a wedge embedded in a gyroelectric medium.