Tucana-II (Tuc-II), a recently discovered and confirmed Ultra Faint Dwarf Spheroidal galaxy, has a high mass to light ratio as well as a large line-of-sight stellar velocity dispersion, thus making it an ideal candidate for an indirect dark matter (DM) search. In this paper, we have analyzed nine years of $gamma$-ray data obtained from the textit{Fermi}-LAT instrument from the direction of Tuc-II. The fact that a very weak significant $gamma$-ray excess ($2.2sigma$) over the background of Tuc-II have been detected from the location of this galaxy. We have observed that this excess of $gamma$-ray emission from the of location Tuc-II rises with longer periods of data. If WIMP pair annihilation is assumed for this faint emission, for $bbar{b}$ annihilation channel the test statistics (TS) value peaks at DM mass $sim$ 14 GeV and for $tau^{+}tau^{-}$ annihilation channel it peaks at DM mass 4 GeV. It is then called for an estimation of the $95%$ confidence level upper limit of the possible velocity weighted self-annihilation cross-section of the DM particles (WIMPs) within Tuc-II by fitting the observed $gamma$-ray flux with spectra expected for DM annihilation. The estimated upper limits of the cross-sections from Tuc-II are then compared with two other dwarf galaxies that are considered to be good DM candidates in several studies. We have also compared our results with the cross-sections obtained in various popular theoretical models of the WIMPs to find that our results impose reasonable tight constraints on the parameter spaces of those DM models. In the concluding section, we compared our results with the similar results obtained from a combined dSph analysis by the textit{Fermi}-LAT collaboration as well as the results obtained from the studies of DM in the dwarf galaxies by the major ground-based Cherenkov experiments.
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