  The size of dust grains, $a$, is key to the physical and chemical processes
in circumstellar disks, but observational constraints of grain size remain
challenging. (Sub)millimeter continuum observations often show a percent-level
polarization parallel to the disk minor axis, which is generally attributed to
scattering by $\sim 100\mu$m-sized spherical grains (with a size parameter $x
\equiv 2\pi a / \lambda < 1$, where $\lambda$ is the wavelength). Larger
spherical grains (with $x$ greater than unity) would produce opposite
polarization direction. However, the inferred size is in tension with the
opacity index $\beta$ that points to larger mm/cm-sized grains. We investigate
the scattering-produced polarization by large irregular grains with a range of
$x$ greater than unity with optical properties obtained from laboratory
experiments. Using the radiation transfer code, RADMC-3D, we find that large
irregular grains still produce polarization parallel to the disk minor axis. If
the original forsterite refractive index in the optical is adopted, then all
samples can produce the typically observed level of polarization. Accounting
for the more commonly adopted refractive index using the DSHARP dust model,
only grains with $x$ of several (corresponding to $\sim$mm-sized grains) can
reach the same polarization level. Our results suggest that grains in disks can
have sizes in the millimeter regime, which may alleviate the tension between
the grain sizes inferred from scattering and other means. Additionally, if
large irregular grains are not settled to the midplane, their strong forward
scattering can produce asymmetries between the near and far side of an inclined
disk, which can be used to infer their presence.
