  A peculiar aspect of Cherenkov telescopes is that they are designed to detect
atmospheric light flashes on the time scale of nanoseconds, being almost blind
to stellar sources. As a consequence, the pointing calibration of these
instruments cannot be done in general exploiting the standard astrometry of the
focal plane. In this paper we validate a procedure to overcome this problem for
the case of the innovative ASTRI telescope, developed by INAF, exploiting sky
images produced as an ancillary output by its novel Cherenkov camera. In fact,
this instrument implements a statistical technique called "Variance method"
(VAR) owning the potentiality to image the star field (angular resolution $\sim
11'$). We demonstrate here that VAR images can be exploited to assess the
alignment of the Cherenkov camera with the optical axis of the telescope down
to $\sim 1''$. To this end, we evaluate the position of the stars with
sub-pixel precision thanks to a deep investigation of the convolution between
the point spread function and the pixel distribution of the camera, resulting
in a transformation matrix that we validated with simulations. After that, we
considered the rotation of the field of view during long observing runs,
obtaining light arcs that we exploited to investigate the alignment of the
Cherenkov camera with high precision, in a procedure that we have already
tested on real data. The strategy we have adopted, inherited from optical
astronomy, has never been performed on Variance images from a Cherenkov
telescope until now, and it can be crucial to optimize the scientific accuracy
of the incoming MiniArray of ASTRI telescopes.
