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Polarized radio emission from PSR J1745−2900 has already been used to investigate the strength of the magnetic field in the Galactic center (GC), close to Sagittarius A*. Here we report how persistent radio emission from this magnetar, for over four years since its discovery, has revealed large changes in the observed Faraday rotation measure (RM), by up to 3500 rad m−2 (a 5% fractional change). From simultaneous analysis of the dispersion measure, we determine that these fluctuations are dominated by variations in either the projected magnetic field or the free electron content within the GC, along the changing line of sight to the rapidly moving magnetar. From a structure function analysis of RM variations, and a recent epoch of rapid change of RM, we determine a minimum scale of magneto-ionic fluctuations of size ∼2 au at the GC distance, inferring PSR J1745−2900 is just ∼0.1 pc behind an additional scattering screen.