  The \textit{Nancy Grace Roman Space Telescope} (\textit{ Roman}) will provide
an enormous number of microlensing light curves with much better photometric
precisions than ongoing ground-based observations. Such light curves will
enable us to observe high-order microlensing effects which have been previously
difficult to detect. In this paper, we investigate \textit{Roman}'s potential
to detect and characterize short-period planets and brown dwarfs (BDs) in
source systems using the orbital motion of source stars, the so-called xallarap
effect. We analytically estimate the measurement uncertainties of xallarap
parameters using the Fisher matrix analysis. We show that the \textit{Roman}
Galactic Exoplanet Survey (RGES) can detect warm Jupiters with masses down to
0.5 $M_{\rm Jup}$ and orbital period of 30 days via the xallarap effect.
Assuming a planetary frequency function from \citet{Cumming+2008}, we find
\textit{Roman} will detect $\sim10$ hot and warm Jupiters and $\sim30$ close-in
BDs around microlensed source stars during the microlensing survey. These
detections are likely to be accompanied by the measurements of the companion's
masses and orbital elements, which will aid in the study of the physical
properties for close-in planet and BD populations in the Galactic bulge.
