The magnetic field structure of the ejecta of a coronal mass ejection (CME) is not known well near the Sun. Here we demonstrate, with a numerical simulation, a relationship between the subsonic plasma flows in the CME-sheath and the ejecta magnetic field direction. We draw an analogy to the outer heliosphere, where Opher et al. used Voyager 2 measurements of the solar wind in the heliosheath to constrain the strength and direction of the local interstellarmagneticfield.Wesimulatethreeejectionswiththesameinitialfreeenergy,butdifferentejectamagnetic field orientations in relation to the global coronal field. Each ejection is launched into the same background solar wind using the Space Weather Modeling Framework. The different ejecta magnetic field orientations cause the CME-pause (the location of pressure balance between solar wind and ejecta material) to evolve differently in the lower corona. As a result, the CME-sheath flow deflections around the CME-pauses are different. To characterize this non-radial deflection, we use θF = tan −1 V N VT , where VN and VT are the normal and tangential plasma flow as measured in a spacecraft-centered coordinate system. Near the CME-pause, we found that θF is very sensitive to the ejecta magnetic field, varying from 45 ◦ to 98 ◦ between the cases when the CME-driven shock is located at 4.5 R� . The deflection angle for each case is found to evolve due to rotation of the ejecta magnetic field. We find that this rotation should slow or stop by 10 R� (also suggested by observational studies). These results indicate that an observational study of CME-sheath flow deflection angles from several events (to account for the interaction with the solar wind), combined with numerical simulations (to estimate the ejecta magnetic field rotation between eruption and 10 R� ) can be used to constrain the ejecta magnetic field in the lower corona.