Direction of arrival (DoA) estimation has wide-ranging applications and is particularly challenging in complex propagation environments. Conventional approaches estimate the DoA based on the phase of the impinging signal on a sensor array. This approach has several challenges: for example, it requires tight synchronization among array elements and the estimated DoA is sensitive to multipath and to correct specification of the array geometry. In this paper, we develop a principled Bayesian DoA estimation algorithm based on the received signal strength gradient. We present algorithms for clustering, spatial- and model-based outlier detection and removal, and proper uncertainty quantification, which yield an estimator robust to non-uniform shadowing, multipath, and errors in antenna position. Physics-based full-wave simulations and experiments in the 2.4 GHz and 40 MHz bands illustrate the utility of our approach.