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Nonequilibrium spin transport in a magnetic tunnel junction comprising a single magnetic layer in the presence of interfacial spin-orbit interaction (SOI) is studied theoretically. The interfacial SOI generates a spin torque of the form T=T||M×(z×;M)+T⊥z×M, even in the absence of an external spin polarizer. For thick and large tunnel barriers, the torque reduces to the perpendicular component T⊥, which can be electrically tuned by applying a voltage across the insulator. In the limit of thin and low tunnel barriers, the in-plane torque T|| emerges, proportional to the tunneling current density. Experimental implications on magnetic devices are discussed.