Theoretical and observational studies suggest that between‐event variability in the median ground motions of larger () earthquakes is controlled primarily by the dynamic properties of the earthquake source, such as Brune‐type stress drop. Analogous results remain equivocal for smaller events due to the lack of comprehensive and overlapping ground‐motion and source‐parameter datasets in this regime. Here, we investigate the relationship between peak ground acceleration (PGA) and dynamic stress drop for a new dataset of 5297 earthquakes that occurred in the San Francisco Bay area from 2002 through 2016. For each event, we measure PGA on horizontal‐component channels of stations within 100 km and estimate stress drop from P‐wave spectra recorded on vertical‐component channels of the same stations. We then develop a nonparametric ground‐motion prediction equation (GMPE) applicable for the moderate (M 1–4) earthquakes in our study region, using a mixed‐effects generalization of the Random Forest algorithm. We use the Random Forest GMPE to model the joint influence of magnitude, distance, and near‐site effects on observed PGA. We observe a strong correlation between dynamic stress drop and the residual PGA of each event, with the events with higher‐than‐expected PGA associated with higher values of stress drop. The strength of this correlation increases as a function of magnitude but remains significant even for smaller magnitude events with corner frequencies that approach the observable bandwidth of the acceleration records. Mainshock events are characterized by systematically higher stress drop and PGA than aftershocks of equivalent magnitude. Coherent local variations in the distribution of dynamic stress drop provide observational constraints to support the future development of nonergodic GMPEs that account for variations in median stress drop at different source locations.