Radon concentrations in soil gas measured in shallow holes by plastic Track Etch detectors show variations which may be associated with four magnitude 4.2 to 4.7 earthquakes on the San Jacinto Fault in southern California. A simple sinusoidal correction for the annual soil temperature cycle removes most of the variability in radon concentration that cannot be correlated with earthquakes. The two earthquakes located approximately 4 and 5.5 km away from the array of detectors showed spatially coherent responses with the largest radon concentration changes occurring closes to the earthquake. The two earthquakes 10--15 km distant from the closest site showed changes apparent when all sites were averaged together. The two nearby earthquakes were right lateral strike-slip events which had quadrants of seismic compression and dilation which correlate with radon concentration increases and decreases, respectively. Radon increases occur when the upward velocity of soil gas increases, since a sharp radon concentration gradient exists in the top few meters of soil. Gas outflow may occur in regions of compression and inflow in areas of dilation, thus producing the observed radon concentration changes.