Controlling magnetization dynamics with a femtosecond laser is attracting interest both in fundamental science and in industry because of the potential to achieve magnetic switching at ever faster speeds. Here, we report a coherent, phase-locked coupling between a high-field single-cycle terahertz transient and the magnetization of ferromagnetic cobalt films. The visualized magnetization dynamics follow the temporal terahertz field oscillation, are tightly locked to the terahertz phase and are induced in the absence of resonant excitations and energy deposition. The magnetic response occurs on the timescale of the stimulus and is thus two orders of magnitude faster than the Larmor precession response. The experimental results are excellently reproduced by the Landau-Lifshift-Gilbert semi-empirical model, indicating its applicability to ultrafast magnetization dynamics and also demonstrating the marginal effect of the co-propagating terahertz electric field. This novel phenomenon of phase-locked control of magnetization with a strong terahertz field suggests new opportunities for ultrafast data storage.