  Creation of stable intrinsically anisotropic self-bound states with embedded
vorticity is a challenging issue. Previously, no such states in Bose-Einstein
condensates (BECs) or other physical settings were known. Dipolar BEC suggests
a unique possibility to predict stable anisotropic vortex quantum droplets
(AVQDs). We demonstrate that they can be created with the vortex' axis oriented
\emph{perpendicular} to the polarization of dipoles. The stability area and
characteristics of the AVQDs in the parameter space are revealed by means of
analytical and numerical methods. Further, the rotation of the polarizing
magnetic field is considered, and the largest angular velocities, up to which
spinning AVQDs can follow the rotation in clockwise and anti-clockwise
directions, are found. Collisions between moving AVQDs are studied too,
demonstrating formation of bound states with a vortex-antivortex-vortex
structure. A stability domain for such stationary bound states is identified.
Unstable dipolar states, that can be readily implemented by means of phase
imprinting, quickly transform into robust AVQDs, which suggests a
straightforward possibility for the creation of these states in the experiment.
