We report on the observation of the $W$-annihilation decay $D^{+}_{s} rightarrow omega pi^{+}$ and the evidence for $D_{s}^{+} rightarrow omega K^{+}$ with a data sample corresponding to an integrated luminosity of 3.19 fb$^{-1}$ collected with the BESIII detector at the center-of-mass energy $sqrt{s} = 4.178$ GeV. We obtain the branching fractions $mathcal{B}(D^{+}_{s} rightarrow omega pi^{+}) = (1.77pm0.32_{{rm stat.}}pm0.11_{{rm sys.}}) times 10^{-3}$ and $mathcal{B}(D^{+}_{s} rightarrow omega K^{+}) = (0.87pm0.24_{{rm stat.}}pm0.07_{{rm sys.}}) times 10^{-3}$, respectively.