Methods to manipulate the magnetization of ferromagnets by means of local electric fields or current-induced spin transfer torque allow the design of integrated spintronic devices with reduced dimensions and energy consumption compared with conventional magnetic field actuation. An alternative way to induce a spin torque using an electric current has been proposed based on intrinsic spin-orbit magnetic fields and recently realized in a strained low-temperature ferromagnetic semiconductor. Here we demonstrate that strong magnetic fields can be induced in ferromagnetic metal films lacking structure inversion symmetry through the Rashba effect. Owing to the combination of spin-orbit and exchange interactions, we show that an electric current flowing in the plane of a Co layer with asymmetric Pt and AlOx interfaces produces an effective transverse magnetic field of 1 T per 108 A cm-2. Besides its fundamental significance, the high efficiency of this process makes it a realistic candidate for room-temperature spintronic applications.