Using the Westerbork Synthesis Radio Telescope (WSRT), we obtained high-time-resolution measurements of the full (linear and circular) polarization of the Crab pulsar. Taken at a resolution of 1/8192 of the 34-ms pulse period (i.e., $4.1~mu{rm s}$), the 1.38-GHz linear-polarization measurements are in general agreement with previous lower-time-resolution 1.4-GHz measurements of linear polarization in the main pulse (MP), in the interpulse (IP), and in the low-frequency component (LFC). We find the MP and IP to be linearly polarized at about $24%$ and $21%$, with no discernible difference in polarization position angle. However, and contrary to theoretical expectations and measurements in the visible, we find no evidence for significant variation (sweep) in polarization position angle over the MP, the IP, or the LFC. Although, the main pulse exhibits a small but statistically significant quadratic variation in the degree of linear polarization. We discuss the implications which appear to be in contradiction to theoretical expectations. In addition, we detect weak circular polarization in the main pulse and interpulse, and strong ($approx 20%$) circular polarization in the low-frequency component, which also exhibits very strong ($approx 98%$) linear polarization at a position angle about $40degree$ from that of the MP or IP. The pulse-mean polarization properties are consistent with the LFC being a low-altitude component and the MP and IP being high-altitude caustic components. Nevertheless, current models for the MP and IP emission do not readily account for the observed absence of pronounced polarization changes across the pulse. Finally, we measure IP and LFC pulse phases relative to the MP that are consistent with recent measurements, which have shown that the phases of these pulse components are evolving with time.
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