The behavior of silicon carbide (SiC) under shock compression is of interest due to its applications as a high-strength ceramic and for general understanding of shock-induced polymorphism. Here we use the Matter in Extreme Conditions beamline of the Linac Coherent Light Source to carry out a series of time-resolved pump-probe x-ray diffraction measurements on SiC laser-shocked to as high as 206 GPa. Experiments on single crystals and polycrystals of different polytypes show a transformation from a low-pressure tetrahedral phase to the high-pressure rocksalt-type (B1) structure. We directly observe coexistence of the low- and high-pressure phases in a mixed-phase region and complete transformation to the B1 phase above 200 GPa. The densities measured by x-ray diffraction are in agreement with both continuum gas-gun studies and a theoretical B1 Hugoniot derived from static-compression data. Time-resolved measurements during shock loading and release reveal a large hysteresis upon unloading, with the B1 phase retained to as low as 5 GPa. The sample eventually reverts to a mixture of polytypes of the low-pressure phase at late times. Our study demonstrates that x-ray diffraction is an effective means to characterize the time-dependent structural response of materials undergoing shock-induced phase transformations at megabar pressures.