  The Polarized Atomic Hydrogen Gas Jet Target polarimeter (HJET) is used to
measure the absolute proton beam polarization,
$\sigma_P^\text{syst}/P\!\lesssim\!0.5\%$, at the Relativistic Heavy Ion
Collider. Here I consider the possibility of employing HJET to measure the
${}^3\text{He}$ ($h$) beam polarization at the Electron-Ion Collider (EIC). The
dominant contribution to the ratio of the $h^\uparrow{p}$ and $p^\uparrow{h}$
analyzing powers, which is needed for such measurements, can be easily
calculated using well-known values of the proton and helion magnetic moments,
but some corrections should be applied to achieve the required accuracy. It was
found that corrections due to absorption and ${}^3\text{He}$ breakup
effectively cancel in the ratio and a correction due to hadronic spin-flip
amplitudes can be derived from the proton beam measurements. As a result, the
anticipated systematic uncertainty in the measured ${}^3\text{He}$ beam
polarization can satisfy the EIC requirement
$\sigma_P^\text{syst}/P\!\lesssim\!1\%$.
