Modeling the transport of “dust” particles in a magnetically confined plasma device is an area of active research and requires a detailed understanding of the forces experienced by dust immersed in a plasma. One of the most significant of these is the “ion drag force.” Dust transport codes employ a model of this force that was not specifically designed for fusion plasmas and so does not consider the relevance of strong magnetic fields. However, it is shown here that the effect of magnetic fields on the ion drag force is significant for such plasmas. In this work, the Monte Carlo code DiMPl is employed to perform the first detailed characterization of the dependence of the ion drag force on magnetic fields. A semi-empirical model of this dependence is fitted onto the simulation data, so that these magnetic effects may be straightforwardly captured by dust transport codes. The limiting behavior of the ion drag force in the case of very strong fields is derived analytically and shown to be consistent with the simulation results. The validity of the results is further motivated through a novel theoretical treatment of the ion drag force at intermediate magnetic field strengths.