We investigate the kinematic properties of Galactic HII regions using radio recombination line (RRL) emission detected by the Australia Telescope Compact Array at 4-10GHz and the Jansky Very Large Array at 8-10GHz. Our HII region sample consists of 425 independent observations of 374 nebulae that are relatively well isolated from other, potentially confusing sources and have a single RRL component with a high signal-to-noise ratio. We perform Gaussian fits to the RRL emission in position-position-velocity data cubes and discover velocity gradients in 178 (42%) of the nebulae with magnitudes between 5 and 200m/s/arcsec. About 15% of the sources also have an RRL width spatial distribution that peaks toward the center of the nebula. The velocity gradient position angles appear to be random on the sky with no favored orientation with respect to the Galactic plane. We craft HII region simulations that include bipolar outflows or solid body rotational motions to explain the observed velocity gradients. The simulations favor solid body rotation since, unlike the bipolar outflow kinematic models, they are able to produce both the large, >40m/s/arcsec, velocity gradients and also the RRL width structure that we observe in some sources. The bipolar outflow model, however, cannot be ruled out as a possible explanation for the observed velocity gradients for many sources in our sample. We nevertheless suggest that most HII region complexes are rotating and may have inherited angular momentum from their parent molecular clouds.