Microwave pulse compressors based on a single resonant cavity operating at polarized modes can be super compact, and corrugated structures can transmit high-power, high-frequency microwave with very low loss. We present an $X$ -band (11.424 GHz) pulse compressor using a corrugated cavity with quarter-wavelength depth corrugations working at polarized HE 1-1-14 modes. The cavity has a high-quality factor ($Q_{0}$) of 116 000 with an inner diameter of less than 7 cm and a length of less than 20 cm, which is more compact compared with smooth spherical and cylindrical cavities for equivalent quality factors. The klystron power can be compressed to a peak power of 150 MW in order to feed two high-gradient accelerating structures designed for the Tsinghua Thomson-scattering X-ray Source (TTX). Theory, design, measurements, and the high-power demonstration of the corrugated pulse compressor are presented in detail. Limitations such as breakdowns and temperature rise of using the corrugated structure as a storage element are also further analyzed. [ABSTRACT FROM AUTHOR]