Power storage devices such as batteries are a crucial part of modern technology. The development and use of batteries has accelerated in the past decades, yet there are only a few techniques that allow gathering vital information from battery cells in a nonivasive fashion. A widely used technique to investigate batteries is electrical impedance spectroscopy (EIS), which provides information on how the impedance of a cell changes as a function of the frequency of applied alternating currents. Building on recent developments of inside-out MRI (ioMRI), a technique is presented here which produces spatially-resolved maps of the oscillating magnetic fields originating from the alternating electrical currents distributed within a cell. The technique works by using an MRI pulse sequence synchronized with a gated alternating current applied to the cell terminals. The approach is benchmarked with a current-carrying wire coil, and demonstrated with commercial and prototype lithium-ion cells. Marked changes in the fields are observed for different cell types.