We investigate experimentally the dynamics of a nonspherical levitated nanoparticle in a 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±0.5×10^{-23} N m at 1×10^{-1} mbar, with an estimated torque sensitivity of 3.6±1.1×10^{-31} N m/sqrt[Hz] at 1×10^{-7} mbar.