  We investigate experimentally the dynamics of a non-spherical levitated
nanoparticle in vacuum. In addition to translation and rotation motion, we
observe the light torque-induced precession and nutation of the trapped
particle. We provide a theoretical model, which we numerically simulate and
from which we derive approximate expressions for the motional frequencies.
Both, the simulation and approximate expressions, we find in good agreement
with experiments. We measure a torque of $1.9 \pm 0.5 \times 10^{-23}$ Nm at $1
\times 10^{-1}$ mbar, with an estimated torque sensitivity of $3.6 \pm 1.1
\times 10^{-31}$ Nm/$\sqrt{\text{Hz}}$ at $1 \times 10^{-7}$ mbar.
