  In this work we study the radiative capture of ${\rm {}^3He}$ on ${\rm
{}^4He}$ within the halo effective field theory (EFT) framework. At leading
order the capture amplitude comprises the initial state $s$-wave strong and
Coulomb interactions summed to all orders. At the same order in the expansion,
leading two-body currents contribute as well. We find delicate cancelations
between the various contributions, and the two-body current contributions can
be replaced by appropriately enhancing the asymptotic normalizations of the
$^7$Be ground and first excited state wave functions. The next-to-leading order
corrections come from the $s$-wave shape parameter and the pure Coulomb
$d$-wave initial state interactions. We fit the EFT parameters to available
scattering data and most recent capture data. Our zero-energy astrophysical
$S$-factor estimate, $S_{34}\sim 0.55$ keV b, is consistent within error bars
with the average in the literature.
