  The centre of our Milky Way harbours the closest candidate for a supermassive
black hole. The source is thought to be powered by radiatively inefficient
accretion of gas from its environment. This form of accretion is a standard
mode of energy supply for most galactic nuclei. X-ray measurements have already
resolved a tenuous hot gas component from which it can be fed. However, the
magnetization of the gas, a crucial parameter determining the structure of the
accretion flow, remains unknown. Strong magnetic fields can influence the
dynamics of the accretion, remove angular momentum from the infalling gas,
expel matter through relativistic jets and lead to the observed synchrotron
emission. Here we report multi-frequency measurements with several radio
telescopes of a newly discovered pulsar close to the Galactic Centre and show
that its unusually large Faraday rotation indicates a dynamically relevant
magnetic field near the black hole. If this field is accreted down to the event
horizon it provides enough magnetic flux to explain the observed emission from
the black hole, from radio to X-rays.
