  Exozodiacal dust, warm debris from comets and asteroids in and near the
habitable zone of stellar systems, reveals the physical processes that shape
planetary systems. Scattered light from this dust is also a source of
background flux which must be overcome by future missions to image Earthlike
planets. This study quantifies the sensitivity of the Nancy Grace Roman Space
Telescope Coronagraph to light scattered by exozodi, the zodiacal dust around
other stars. Using a sample of 149 nearby stars, previously selected for
optimum detection of habitable exoplanets by space observatories, we find the
maximum number of exozodiacal disks with observable \textit{inner} habitable
zone boundaries is six and the number of observable outer habitable boundaries
is 74. One zodi was defined as the visible-light surface brightness of 22
$m_{\rm V}\ $arcsec$^{-2}$ around a solar-mass star, approximating the
scattered light brightness in visible light at the Earth-equivalent insolation.
In the speckle limited case, where the signal-to-noise ratio is limited by
speckle temporal stability rather than shot noise, the median $5\sigma$
sensitivity to habitable zone exozodi is 12 zodi per resolution element. This
estimate is calculated at the inner-working angle of the coronagraph, for the
current best estimate performance, neglecting margins on the uncertainty in
instrument performance and including a post-processing speckle suppression
factor. For an log-norm distribution of exozodi levels with a median exozodi of
3$\times$ the solar zodi, we find that the Roman Coronagraph would be able to
make 5$\sigma$ detections of exozodiacal disks in scattered light from 13
systems with a 95\% confidence interval spanning 7-20 systems. This sensitivity
allows Roman Coronagraph to complement ground-based measurements of exozodiacal
thermal emission and constrain dust albedos.
