With the advancement of magnetization-based spintronic applications, there has been considerable interest in spin-orbit torque as an electric technique to dynamically manipulate magnetization. In this study, gate-induced ON-OFF switchable spin-orbit torque in Pt/Co/Pt spin-orbit device using the ionic gating technique is reported. By canceling the spin currents from Pt layers, the OFF state is attained in Pt/Co/Pt spin-orbit device. Notably, under a strong negative gate electric field applied to the Pt/Co/Pt spin-orbit device, the damping-like spin-orbit torque is markedly enhanced over sixfold compared with the applied positive gate electric field. We show that the gate modulation of the spin-orbit torque in the Pt/Co/Pt spin-orbit device can be explained by considering the change of the spin-charge interconversion by electric gating. This research serves as a promising avenue for electrically programmable spintronic devices.