  The existence of stationary solutions of the Einstein-Vlasov-Maxwell system
which are axially symmetric but not spherically symmetric is proven by means of
the implicit function theorem on Banach spaces. The proof generalises the
methods of an article by H{\aa}kan Andr\'easson, Markus Kunze and Gerhard Rein
where a similar result is obtained for uncharged particles. Among the solutions
constructed in this article there are rotating and non-rotating ones. Static
solutions exhibit an electric but no magnetic field. In the case of rotating
solutions, in addition to the electric field, a purely poloidal magnetic field
is induced by the particle current. The existence of toroidal components of the
magnetic field turns out to be not possible in this setting.
