Strong singly-ionized magnesium ( MgII ) absorption lines in quasar spectra typically serve as a proxy for intervening galaxies along the line of sight . Previous studies have found a correlation between the number of these MgII absorbers and the Faraday rotation measure ( RM ) at \approx 5 GHz . We cross-match a sample of 35,752 optically-identified non-intrinsic MgII absorption systems with 25,649 polarized background radio sources for which we have measurements of both the spectral index and RM at 1.4 GHz . We use the spectral index to split the resulting sample of 599 sources into flat-spectrum and steep-spectrum subsamples . We find that our flat-spectrum sample shows significant ( \sim 3.5 \sigma ) evidence for a correlation between MgII absorption and RM at 1.4 GHz , while our steep-spectrum sample shows no such correlation . We argue that such an effect can not be explained by either luminosity or other observational effects , by evolution in another confounding variable , by wavelength-dependent polarization structure in an active galactic nucleus , by the Galactic foreground , by cosmological expansion , or by partial coverage models . We conclude that our data are most consistent with intervenors directly contributing to the Faraday rotation along the line of sight , and that the intervening systems must therefore have coherent magnetic fields of substantial strength ( \bar { B } = 1.8 \pm 0.4 \upmu G ) . Nevertheless , the weak nature of the correlation will require future high-resolution and broadband radio observations in order to place it on a much firmer statistical footing .