Spin-orbit torques (SOTs) in multilayers of ferromagnetic (FM) and non-magnetic (NM) metals can manipulate the magnetization of the FM layer efficiently. This is employed, for example, in non-volatile magnetic memories for energy-efficient mobile electronics(1,2) and spin torque nano-oscillators(3-7) for neuromorphic computing(8). Recently, spin torque nano-oscillators also found use in microwave-assisted magnetic recording, which enables ultrahigh-capacity hard disk drives(9). Most SOT devices employ spin Hall(10,11) and Rashba(12) effects, which originate from spin-orbit coupling within the NM layer and at the FM/NM interfaces, respectively. Recently, SOTs generated by the anomalous Hall effect in FM/NM/FM multilayers were predicted(13) and experimentally realized(14). The control of SOTs through crystal symmetry was demonstrated as well(15). Understanding all the types of SOTs that can arise in magnetic multilayers is needed for a formulation of a comprehensive SOT theory and for engineering practical SOT devices. Here we show that a spin-polarized electric current known to give rise to anisotropic magnetoresistance (AMR) and the planar Hall effect (PHE) in a FM16 can additionally generate large antidamping SOTs with an unusual angular symmetry in NM1/FM/NM2 multilayers. This effect can be described by a recently proposed magnonic mechanism(17). Our measurements reveal that this torque can be large in multilayers in which both spin Hall and Rashba torques are negligible. Furthermore, we demonstrate the operation of a spin torque nano-oscillator driven by this SOT. These findings significantly expand the class of materials that exhibit giant SOTs.