Instruments flown on CubeSats are small. Meaningful applications of CubeSats in astronomical observations rely on the choice of a particular subject that is feasible for CubeSats. Here we report the result of a feasibility study for observing gamma-ray polarization from Cygnus X-1 using a small Compton polarimeter on board a 3U CubeSat. Silicon detectors and cerium bromide scintillators were employed in the instrument models that we discussed in this study. Through Monte Carlo simulations with Geant4-based MEGALib package, we found that, with 10-Ms observation time in a low earth orbit, the minimum detectable polarization degree can be lower than 10% in 100 -250 keV, 20% in 250 -400 keV, and 65% in 400 -2000 keV, if the instrument trigger energy threshold is set at 40 keV. A 3U CubeSat dedicated to observing Cygnus X-1 can therefore yield useful information on the polarization state of gamma-ray emissions from the brightest persistent X-ray black-hole binary in the sky.