Impulsive radio signals such as fast radio bursts (FRBs) are imprinted with the signatures of multi-path propagation through ionised media in the form of frequency-dependent temporal broadening of the pulse profile, commonly referred to as scattering. The dominant source of scattering for most FRBs is expected to be within their host galaxies, an assumption which can be tested by examining potential correlations between the scattering properties of the FRBs and global properties of their hosts. Using results from the Commensal Real-time ASKAP Fast Transient (CRAFT) survey, we investigate correlations across a range of host galaxy properties against attributes of the FRB that encode propagation effects: scattering timescale
$\tau$, polarisation fractions, and absolute Faraday rotation measure. From 21 host galaxy properties considered, we find three that are correlated with
$\tau$, including the stellar surface density (or compactness; Pearson’s p-value p = 0.002 and Spearman’s p = 0.010), the mass-weighted age (Spearman’s p-value p = 0.009), and a weaker correlation with the gas-phase metallicity (Spearman’s
$p = 0.017$). Weakly significant correlations are also found with
$H\alpha$ equivalent widths and stellar gravitational potential. From 10 000 trials of reshuffled datasets, we expect two strong Spearman’s correlations only 2% of the time and three weaker correlations in 6.6% of cases. Compact host galaxies may have more ionised content which scatters the FRB further. Compact galaxies were also found to correlate with gas-phase metallicity in our sample, while H ii regions along the line-of-sight are also a potential contributing factor. No correlation is seen with host galaxy inclination, which weakens the case for an inclination bias, as previously suggested for samples of localised FRBs. A strong (
$p = 0.002$) correlation is found for absolute rotation measure with optical disc axis ratio b/a; greater rotation measures are seen for edge-on host galaxies. Further high-time resolution FRB detections, coupled with localisation and detailed follow-up on their host galaxies, are necessary to corroborate these initial findings and shed further light into the FRB mechanism.