Although disk accretion onto compact objects-white dwarfs, neutron stars and black holes-is central to much of high-energy astrophysics, the mechanisms that enable this process have remained observationally difficult to determine. Accretion disks must transfer angular momentum in order for matter to travel radially inward onto the compact object. Internal viscosity from magnetic processes and disk winds can both in principle transfer angular momentum, but hitherto we lacked evidence that either occurs. Here we report that an X-ray-absorbing wind discovered in an observation of the stellar-mass black hole binary GRO J1655 - 40 (ref. 6) must be powered by a magnetic process that can also drive accretion through the disk. Detailed spectral analysis and modelling of the wind shows that it can only be powered by pressure generated by magnetic viscosity internal to the disk or magnetocentrifugal forces. This result demonstrates that disk accretion onto black holes is a fundamentally magnetic process.