We have employed time-resolved X-ray diffraction with picosecond temporal resolution to measure the time-dependent rocking curves of laser-irradiated asymmetrically cut single InSb crystals. Coherent acoustic phonons were excited in the crystals by irradiation with 800-nm, 100-fs laser pulses at irradiances between 0.25 and 12 mJ/cm. The induced time-dependent strain profiles (corresponding to the coherent phonons) were monitored by diffracting collimated, monochromatic pulses of X-rays from the irradiated crystals. Recording of the diffracted radiation with a fast low-jitter X-ray streak camera resulted in an overall temporal resolution of better than 2 ps. The strain associated with the coherent phonons modifies the rocking curve of the crystal in a time-dependent manner, and the rocking curve is recorded by keeping the angle of incidence of the X-rays upon the crystal fixed, but varying the energy of the incident X-rays around a central energy of 8.453 keV (corresponding to the peak of the rocking curve of the unperturbed crystal). The observed time-dependent diffraction from the irradiated crystals is in reasonable agreement with simulations over a wide range of energies from the unperturbed rocking-curve peak.