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 companions 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.
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