Faraday rotation measures (RMs) of fast radio bursts (FRBs) offer the
prospect of directly measuring extragalactic magnetic fields. We present an
analysis of the RMs of ten as yet non-repeating FRBs detected and localized to
host galaxies by the 110-antenna Deep Synoptic Array (DSA-110). We combine this
sample with published RMs of 15 localized FRBs, nine of which are repeating
sources. For each FRB in the combined sample, we estimate the host-galaxy
dispersion measure (DM) contributions and extragalactic RM. We find compelling
evidence that the extragalactic components of FRB RMs are often dominated by
contributions from the host-galaxy interstellar medium (ISM). Specifically, we
find that both repeating and as yet non-repeating FRBs show a correlation
between the host-DM and host-RM in the rest frame, and we find an
anti-correlation between extragalactic RM (in the observer frame) and redshift
for non-repeaters, as expected if the magnetized plasma is in the host galaxy.
Important exceptions to the ISM origin include a dense, magnetized circum-burst
medium in some repeating FRBs, and the intra-cluster medium (ICM) of host or
intervening galaxy clusters. We find that the estimated ISM magnetic-field
strengths, B∣∣​, are characteristically larger than those inferred from
Galactic radio pulsars. This suggests either increased ISM magnetization in FRB
hosts in comparison with the Milky Way, or that FRBs preferentially reside in
regions of increased magnetic-field strength within their hosts