2I/Borisov is the first and only unambiguous comet to date definitively identified as originating from beyond the solar system, and its dust grains offer insight into properties of the comet nucleus and the extrasolar environment in which it formed. Polarization is a characteristic of scattered light directly related to the composition, shape and structure of scattering particles, and provides a unique way to remotely probe these grains and their physical evolution through the coma radiation environment. We used the Hubble Space Telescope (HST) to collect imaging polarimetry of 2I/Borisov’s inner coma over seven epochs from 2019 November 25 to 2020 May 9 at phase angles between 12 and 29 degrees and heliocentric distances between 2.0 and 3.9 au. Results show the dust polarization within 500 km of the nucleus to be broadly consistent with the range of total dust coma polarization measured for local solar system comets over similar phase angles. However, we do not find any region of locally elevated positive polarization surrounding the nucleus, as was previously observed by HST on the Oort cloud comet C/2012 S1 (ISON) before perihelion under otherwise similar observing circumstances to our last epoch. We also do not measure any dust with negative polarization as strong as observed in the circumnucleus halos of many comets at similarly low phase angles.