Solar-cycle-related variation of the solar chromospheric rotation is studied by analyzing the chromospheric rotation rate of 938 synoptic maps generated from the Ca ii K line at the Mount Wilson Observatory during the period of 1915 August 10 to 1985 July 7. The results obtained are as follows: (1) The parameters A (the equatorial rotation rate) and B (the latitudinal gradient of rotation) in the standard form of differential rotation both show a decreasing trend in the considered time frame, although A has weak statistical significance. (2) There is a significant negative correlation between the level of solar activity and parameter B, indicating that there seems to be a correlation between field strength and chromospheric differential rotation. (3) During solar cycles 15, 16, 19, 20, and 21, the southern hemisphere rotates faster, whereas in cycles 17 and 18, the northern hemisphere rotates faster. (4) There exists a significant negative correlation between the N-S asymmetry of the chromospheric rotation rate and that of solar activity, indicating that differential rotation of the chromosphere seems to be strengthened by stronger magnetic activity in a certain hemisphere. Possible explanations for the above results are given.