In this work, isogeometric mortaring is used for the simulation of a six-pole permanent magnet synchronous machine. Isogeometric mortaring is especially well suited for the efficient computation of rotating electric machines, as it allows for an exact geometry representation for arbitrary rotation angles without the need for remeshing. The appropriate B-spline spaces needed for the solution of Maxwell's equations and the corresponding mortar spaces are introduced. Unlike classical finite-element methods (FEMs), their construction is straightforward in the isogeometric case. The torque in the machine is computed using two different methods, that is, Arkkio's method and using the Lagrange multipliers from the mortaring.