Tracking the excitation of water molecules in the homogeneous liquid is challenging due to the ultrafast dissipation of rotational excitation energy through the hydrogen-bonded network. Here we demonstrate strong transient anisotropy of liquid water through librational excitation using single-color pump-probe experiments at 12.3 THz. We deduce a third-order response of χ3 exceeding previously reported values in the optical range by 3 orders of magnitude. Using a theory that replaces the nonlinear response with a material property amenable to molecular dynamics simulation, we show that the rotationally damped motion of water molecules in the librational band is resonantly driven at this frequency, which could explain the enhancement of the anisotropy in the liquid by the external terahertz field. By addition of salt (MgSO4), the hydration water is instead dominated by the local electric field of the ions, resulting in reduction of water molecules that can be dynamically perturbed by THz pulses.