  The slitless grism on the Nancy Grace Roman Space Telescope will enable deep
near-infrared spectroscopy over a wide field of view. We demonstrate Roman's
capability to detect Ly$\alpha$ galaxies at $z>7$ using a multi-position-angle
(PA) observational strategy. We simulate Roman grism data using a realistic
foreground scene from the COSMOS field. We also input fake Ly$\alpha$ galaxies
spanning redshift z=7.5-10.5 and a line-flux range of interest. We show how a
novel data cube search technique -- CUBGRISM -- originally developed for GALEX
can be applied to Roman grism data to produce a Ly$\alpha$ flux-limited sample
without the need for continuum detections. We investigate the impact of
altering the number of independent PAs and exposure time. A deep Roman grism
survey with 25 PAs and a total exposure time of $70$hrs can achieve Ly$\alpha$
line depths comparable to the deepest $z=7$ narrow-band surveys
($L_{{\rm{Ly}}\alpha}\gtrsim10^{43}$erg s$^{-1}$). Assuming a null result,
where the opacity of the intergalactic medium (IGM) remains unchanged from
$z\sim7$, this level of sensitivity will detect $\sim400$ deg$^{-2}$ Ly$\alpha$
emitters from $z=7.25-8.75$. A decline from this expected number density is the
signature of an increasing neutral hydrogen fraction and the onset of
reionization. Our simulations indicate that a deep Roman grism survey has the
ability to measure the timing and magnitude of this decline, allowing us to
infer the ionization state of the IGM and helping us to distinguish between
models of reionization.
