  Recent ALMA observations indicate that CW Leo, the closest carbon-rich AGB
star to the Sun, might have a low-mass stellar companion. We present archival
ground-based astrometric measurements of CW Leo obtained within the context of
the Torino Parallax Program and with $>6$ yr ($1995 - 2001$) of time baseline.
The residuals to a single-star solution show significant curvature, and they
are strongly correlated with the well-known $I$-band photometric variations due
to stellar pulsations. We describe successfully the astrometry of CW Leo with a
variability-induced motion (VIM) + acceleration model. We obtain proper motion
and parallax of the center-of-mass of the binary, the former in fair agreement
with recent estimates, the latter at the near end of the range of inferred
distances based on indirect methods. The VIM + acceleration model results allow
us to derive a companion mass in agreement with that inferred by ALMA, they
point towards a somewhat longer period than implied by ALMA, but are not
compatible with much longer period estimates. These data will constitute a
fundamental contribution towards the full understanding of the orbital
architecture of the system when combined with Gaia astrometry, providing a
$\sim 25$\,yr time baseline.
