Statistical properties of Faraday rotation measure in external galaxies
  -- I: intervening disc galaxies
  Deriving the Faraday rotation measure (RM) of quasar absorption line systems,
which are tracers of high-redshift galaxies intervening background quasars, is
a powerful tool for probing magnetic fields in distant galaxies. Statistically
comparing the RM distributions of two quasar samples, with and without
absorption line systems, allows one to infer magnetic field properties of the
intervening galaxy population. Here, we have derived the analytical form of the
probability distribution function (PDF) of RM produced by a single galaxy with
an axisymmetric large-scale magnetic field. We then further determine the PDF
of RM for one random sight line traversing each galaxy in a population with a
large-scale magnetic field prescription. We find that the resulting PDF of RM
is dominated by a Lorentzian with a width that is directly related to the mean
axisymmetric large-scale field strength $\langle B_0 \rangle$ of the galaxy
population if the dispersion of $B_0$ within the population is smaller than
$\langle B_0 \rangle$. Provided that RMs produced by the intervening galaxies
have been successfully isolated from other RM contributions along the line of
sight, our simple model suggests that $\langle B_0 \rangle$ in galaxies probed
by quasar absorption line systems can be measured within $\approx50$ per cent
accuracy without additional constraints on the magneto-ionic medium properties
of the galaxies. Finally, we discuss quasar sample selection criteria that are
crucial to reliably interpret observations, and argue that within the
limitations of the current database of absorption line systems,
high-metallicity damped Lyman-$\alpha$ absorbers are best suited to study
galactic dynamo action in distant disc galaxies.
