Fuzzy Dark Matter (FDM) is one of the recent models for dark matter. According to this model, dark matter is made of very light scalar particles with considerable quantum mechanical effects on the galactic scale, which solves many problems of the cold dark matter (CDM)... Here we use the observed data from the rotation curve of the Milky Way (MW) Galaxy to compare the results from FDM and CDM models. We show FDM adds a local peak on the rotation curve close to the center of the bulge, where its position and amplitude depend on the mass of FDM particles. By fitting the observed rotation curve with our expectation from FDM, we find that the mass of FDM is $m = 2.5^{+3.6}_{-2.0} \times10^{-21}$eV. We note that the local peak of the rotation curve in MW can also be explained in the CDM model with an extra inner bulge model for the MW Galaxy. We conclude that the FDM model explains this peak without a need for extra structure for the bulge. (read more)