The spin Hall effect couples charge and spin transport(1-3), enabling electrical control of magnetization (4-)(5). A quintessential example of spin-Hall-related transport is the anomalous Hall effect (AHE)(6), first observed in 1880, in which an electric current perpendicular to the magnetization in a magnetic film generates charge accumulation on the surfaces. Here, we report the observation of a counterpart of the AHE that we term the anomalous spin-orbit torque (ASOT), wherein an electric current parallel to the magnetization generates opposite spin-orbit torques on the surfaces of the magnetic film. We interpret the ASOT as being due to a spin-Hall-like current generated with an efficiency of 0.053 +/- 0.003 in Ni-80 Fe-20, comparable to the spin Hall angle of Pt-7. Similar effects are also observed in other common ferromagnetic metals, including Co, Ni and Fe. First-principles calculations corroborate the order of magnitude of the measured values. This work suggests that a strong spin current with spin polarization transverse to the magnetization can be generated within a ferromagnet, despite spin dephasings(8). The large magnitude of the ASOT should be taken into consideration when investigating spin-orbit torques in ferromagnetic/nonmagnetic bilayers.