  We have observed short-lived optical birefringence in a CH$_3$NH$_3$PbBr$_3$
single crystal induced by a powerful nearly single-cycle terahertz pulse. Apart
from the instantaneous contribution that follows the profile of the squared
pump electric field, the recorded anisotropy signal contains an exponential
component decaying in $\sim$ 350 fs, underdamped oscillations at the frequency
of $\sim$ 0.16 THz and an intermediate picosecond relaxation process with a
Gaussian tail. We associate these three non-trivial features with,
respectively, Kerr effect in the inorganic lattice, terahertz-induced transient
alignment of CH$_3$NH$_3^+$ cations, and their coherent rotation excited by the
terahertz pulse in a Raman process.
