  The existence of stationary solutions to the Einstein-Vlasov system which are
axially symmetric and have non-zero total angular momentum is shown. This
provides mathematical models for rotating, general relativistic and
asymptotically flat non-vacuum spacetimes. If angular momentum is allowed to be
non-zero, the system of equations to solve contains one semilinear elliptic
equation which is singular on the axis of rotation. This can be handled very
efficiently by recasting the equation as one for an axisymmetric unknown on
$\R^5$.
