The Nancy Grace Roman Space Telescope, scheduled to launch in late 2025, will be capable of precision astrometry using its wide field imager. For bright stars, Roman may be able to achieve astrometric accuracy of 1-10 μas. We have simulated an observing program that combines Roman astrometry observations with radial velocity measurements. Astrometry and radial velocity measurements are complementary: radial velocity measurements are most sensitive to planets close to its host star, while the astrometric signal is largest for more distant planets. Astrometric measurements can also break the mass-inclination degeneracy in radial velocity observations. Our simulations are based on the observing program of the Terra Hunting Experiment, which will take nightly Doppler radial velocity observations (starting in 2022) of Sun-like stars in search of planets that are Earth-like in mass and temperature. We also discuss how Roman astrometry could lead to the discovery of companion planets not directly detectable from radial velocity observations alone.