  Weak gravitational lensing is a powerful statistical tool for probing the
growth of cosmic structure and measuring cosmological parameters. However, as
shown by studies such as M\'enard et al. (2010), dust in the circumgalactic
region of haloes dims and reddens background sources. In a weak lensing
analysis, this selects against sources behind overdense regions; since there is
more structure in overdense regions, we will underestimate the amplitude of
density perturbations $\sigma_8$ if we do not correct for the effects of
circumgalactic dust. To model the dust distribution we employ the halo model.
Assuming a fiducial dust mass profile based on measurements from M\'enard et
al. (2010), we compute the ratio $Z$ of the systematic error to the statistical
error for a survey similar to the Nancy Grace Roman Space Telescope reference
survey (2000 deg$^2$ area, single-filter effective source density 30 galaxies
arcmin$^{-2}$). For a waveband centered at $1580$ nm ($H$-band), we find that
$Z_{H} = 0.37$. For a similar survey with waveband centered at $620$ nm
($r$-band), we also computed $Z_{r} = 2.8$. Within our fiducial dust model,
since $Z_{r} > 1$, the systematic effect of dust will be significant on weak
lensing image surveys. We also computed the dust bias on the amplitude of the
power spectrum, $\sigma_{8}$, and found it to be for each waveband $\Delta
\sigma_8/\sigma_8 = -3.1\times 10^{-4}$ ($H$ band) or $-2.2\times 10^{-3}$ ($r$
band) if all other parameters are held fixed (the forecast Roman
statistical-only error $\sigma(\sigma_8)/\sigma_8$ is $9\times 10^{-4}$).
