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The electrical manipulation of magnetization by current-induced spin torques has given access to realize a plethora of ultralow power and fast spintronic devices such as non-volatile magnetic memories, spin-torque nano-oscillators, and neuromorphic computing devices. Recent advances have led to the notion that relativistic spin-orbit coupling is an efficient source for current-induced torques, opening the field of spin-orbitronics. Despite the significant progress, however, the fundamental mechanism of magnetization manipulation, the requirement of spin currents in generating current-induced torques, has remained unchanged. Here, we demonstrate the generation of current-induced torques without the use of spin currents. By measuring the current-induced torque for naturally-oxidized-Cu/ferromagnetic-metal bilayers, we observed an exceptionally high effective spin Hall conductivity at low temperatures despite the absence of strong spin-orbit coupling. Furthermore, we found that the direction of the torque depends on the choice of the ferromagnetic layer, which counters the conventional understanding of the current-induced torque. These unconventional features are best interpreted in terms of an orbital counterpart of the spin torque, an orbital torque, which arises from the orbital Rashba effect and orbital current. These findings will shed light on the underlying physics of current-induced magnetization manipulation, potentially altering the landscape of spin-orbitronics.