This paper proposes a torque vectoring strategy for the propulsion of an electric vehicle with two independent electric machines at the front wheels. The torque vectoring controller includes a vehicle dynamics controller and a motor torque and wheel slip limiter. The nonlinear vehicle dynamics controller is designed as Linear Parameter-Varying (LPV) gain-scheduled controller for tracking the longitudinal velocity and the yaw rate of the vehicle. A linearly interpolated Torque and Slip Limiter (TSL) is derived to cope with saturation of the electric motors and wheel slip limitations. The TSL is based on an extension of a linear time-invariant anti-windup scheme to fit the proposed LPV controller, and uses available wheel slip information to prevent wheel spinning or blocking. A nonlinear 14-degree-of-freedom vehicle model with an advanced Dugoff tire model has been calibrated with real measurement data. This model is used to simulate the closed-loop vehicle behavior. Simulation results show good vehicle dynamics and safety properties.