  The High Latitude Survey of the Nancy Grace Roman Space Telescope is expected
to measure the positions and shapes of hundreds of millions of galaxies in an
area of 2220 deg$^2$. This survey will provide high-quality weak lensing data
with unprecedented systematics control. The Roman Space Telescope will survey
the sky in near infrared (NIR) bands using Teledyne H4RG HgCdTe photodiode
arrays. These NIR arrays exhibit an effect called persistence: charges that are
trapped in the photodiodes during earlier exposures are gradually released into
later exposures, leading to contamination of the images and potentially to
errors in measured galaxy properties such as fluxes and shapes. In this work,
we use image simulations that incorporate the persistence effect to study its
impact on galaxy shape measurements and weak lensing signals. No significant
spatial correlations are found between the galaxy shape changes induced by
persistence. On the scales of interest for weak lensing cosmology, the effect
of persistence on the weak lensing correlation function is about two orders of
magnitude lower than the Roman Space Telescope additive shear error budget,
indicating that the persistence effect is expected to be a subdominant
contributor to the systematic error budget for weak lensing with the Roman
Space Telescope given its current design.
