  Macronovae (or kilonovae) are the optical and NIR counterparts of binary
neutron star mergers. While the macronova in GW170817 was detected about 10
hours after the GW detection, future observations can possibly detect them
within the first hour after the merger. Early- time macronovae are potentially
powered by some mechanisms such as the beta-decay heating of the surviving free
neutrons. In this paper, we propose that the polarimetric observation can be a
useful tool to study the early macronova emissions. If free nucleons remain in
the outermost layer of the ejecta, the electron scattering produces a larger
polarization than that by the r-process element-rich ejecta. The degree of
polarization can show a large value of $\sim3\%$ for the first $0.3-1$ hour for
the free nucleon mass of $10^{-5}-10^{-4}\,M_{\odot}$. Quick polarimetric
observations enable us to study not only the aspherical morphology of the
ejecta but also the amount of the free nucleons in the ejecta, which is helpful
to discriminate the emission mechanisms of the early macronovae.
