  The optical Faraday effect describes the rotation of linear polarization upon
propagation through a medium in the presence of a longitudinal magnetic field.
The effect arises from a different phase delay between the right and left
handed polarisation components of the light. In this paper we predict a Faraday
effect for a completely different system: electron vortices. Free electron
vortex states were recently observed in transmission electron microscopy
experiments, and they introduce new degrees of freedom into the probing of
matter with electron beams. We associate a rotation of a vortex superposition
with the fact that different phases are acquired by oppositely handed vortices
propagating in a magnetic field. We show that, in contrast to the optical
Faraday effect, the rotation of the electron beam occurs in vacuum and arises
from the intrinsic chirality of the constituent vortex states.
