Large earthquakes are usually modeled with simple planar fault surfaces or a combination of several planar fault segments. However, in general, earthquakes occur on faults that are non-planar and exhibit significant geometrical variations in both the along-strike and down-dip directions at all spatial scales. Mapping of surface fault ruptures and high-resolution geodetic observations are increasingly revealing complex fault geometries near the surface and accurate locations of aftershocks often indicate geometrical complexities at depth. With better geodetic data and observations of fault ruptures, more details of complex fault geometries can be estimated resulting in more realistic fault models of large earthquakes. To address this topic, we here parametrize non-planar fault geometries with a set of polynomial parameters that allow for both along-strike and down-dip variations in the fault geometry. Our methodology uses Bayesian inference to estimate the non-planar fault parameters from geodetic data, yielding an ensemble of plausible models that characterize the uncertainties of the non-planar fault geometry and the fault slip. The method is demonstrated using synthetic tests considering slip spatially distributed on a single continuous finite non-planar fault surface with varying dip and strike angles both in the down-dip and along-strike directions. The results show that fault-slip estimations can be biased when a simple planar fault geometry is assumed in presence of significant non-planar geometrical variations. Our method can help to model earthquake fault sources in a more realistic way and may be extended to include multiple non-planar fault segments or other geometrical fault complexities.