  Polarised radio emission from PSR J1745-2900 has already been used to
investigate the strength of the magnetic field in the Galactic Centre, 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, by up to 3500 rad m$^{-2}$ (a five
per cent fractional change). From simultaneous analysis of the dispersion
measure, we determine that these fluctuations are dominated by variations in
the projected magnetic field, rather than the integrated free electron density,
along the changing line of sight to the rapidly moving magnetar. From a
structure function analysis of rotation measure variations, and a recent epoch
of rapid change of rotation measure, we determine a minimum scale of magnetic
fluctuations of size ~ 2 au at the Galactic Centre distance, inferring PSR
J1745-2900 is just ~ 0.1 pc behind an additional scattering screen.
