  We report on the observation of the scissors mode of a single dipolar quantum
droplet. The existence of this mode is due to the breaking of the rotational
symmetry by the dipole-dipole interaction, which is fixed along an external
homogeneous magnetic field. By modulating the orientation of this magnetic
field, we introduce a new spectroscopic technique for studying dipolar quantum
droplets. This provides a precise probe for interactions in the system allowing
to extract a background scattering length for \textsuperscript{164}Dy of
$69(4)\,a_0$. Our results establish an analogy between quantum droplets and
atomic nuclei, where the existence of the scissors mode is also only due to
internal interactions. They further open the possibility to explore physics
beyond the available theoretical models for strongly-dipolar quantum gases.
