We perform experimental quantum polarimetry using a heralded single photon to analyze the optical activity of linearly polarized light traversing a chiral medium. Three kinds of estimators are considered to estimate the concentrations of sucrose solutions from measuring the rotation angle of the linear polarization of the output photons. Through repetition of independent and identical measurements performed for each individual scheme and different concentration sucrose solutions, we compare the estimation uncertainty among the three schemes. The results are also compared to classical benchmarks for which a coherent state of light is taken into account. The quantum enhancement in the estimation uncertainty is evaluated and the impact of experimental and technical imperfections is discussed. In this work, we lay out a route for future applications relying on quantum polarimetry.