Electrically controllable nonvolatile magnetic memories show great potential for the replacement of conventional semiconductor-based memory technologies. Here, we experimentally demonstrate ultrafast spin-orbit torque (SOT)-induced coherent magnetization switching dynamics in a ferromagnet. We use an ultrafast photoconducting switch and a coplanar strip line to generate and guide a ~9-picosecond electrical pulse into a heavy metal/ferromagnet multilayer to induce ultrafast SOT. We then use magneto-optical probing to investigate the magnetization dynamics with sub-picosecond resolution. Ultrafast heating by the approximately 9 picosecond current pulse induces a thermal anisotropy torque which, in combination with the damping-like torque, coherently rotates the magnetization to obtain zero-crossing of magnetization in ~70 picoseconds. A macro-magnetic simulation coupled with an ultrafast heating model agrees well with the experiment and suggests coherent magnetization switching without any incubation delay on an unprecedented time scale. Our work proposes a unique magnetization switching mechanism toward markedly increasing the writing speed of SOT magnetic random-access memory devices.