  Probing magnetic fields in high-redshift galactic systems is crucial to
investigate galactic dynamics and evolution. Utilizing the rotation measure of
the background quasars, we have developed a radial profile of the magnetic
field in a typical high-$z$ galaxy. We have compiled a catalog of 59 confirmed
quasar sightlines, having one intervening Mg \rom{2} absorber in the redshift
range $0.372\leq z_{\text{abs}} \leq 0.8$. The presence of the foreground
galaxy is ensured by comparing the photometric and spectroscopic redshifts
within $3 \sigma_{z-\text{photo}}$ and visual checks. These quasar
line-of-sights (LoS) pass through various impact parameters (D) up to $160$
kpc, covering the circumgalactic medium of a typical Milky-Way type galaxy.
Utilizing the residual rotation measure (RRM) of these sightlines, we estimated
the excess in RRM dispersion, $\sigma_{\text{ex}}^{\text{RRM}}$. We found that
the sightlines having impact parameters $\text{D} \leq 50$ kpc and $\text{D} >
50$ kpc, $\sigma_{\text{ex}}^{\text{RRM}}$ show significant difference from
$24.86 \pm 3.08$ rad m$^{-2}$ to $16.34 \pm 1.88$ rad m$^{-2}$ respectively.
The profile of $\sigma_{\text{ex}}^{\text{RRM}}$ with D exhibits a decreasing
trend. We translated $\sigma_{\text{ex}}^{\text{RRM}}$ to average LoS magnetic
field strength, $\langle B_{\|}\rangle$ by considering a typical electron
column density. Consequently, the anti-correlation is sustained, resulting in a
decreasing magnetic field profile. This suggests a clear indication of varying
magnetic field from the disk to the circumgalactic medium. This work provides a
methodology that, when applied to ongoing and future radio polarisation surveys
such as LOFAR and SKA, promises to significantly enhance our understanding of
magnetic field mapping in galactic systems.
