The study of weak radiative decays of charmed mesons is still in its developing stage. In the Standard Model (SM), the physics of charm mesons is not generally expected to have New Physics (NP) discovery potential. The weak decays of $D$ mesons are difficult to investigate due to significant final-state interactions. However, decays mediated by $c \rightarrow u \gamma$ transitions can be affected by potential contributions coming from the non-minimal supersymmetry, which is an NP scenario. The ratio of branching fractions for radiative $D^{0}$ decays could be violated already in the SM framework, while a similar ratio for $D_{s}^{+}$ radiative decays offers much better prospects for NP. We present herein a sensitivity study of the radiative charm decays $D_{s}^{+}\rightarrow \rho^+ \gamma$ and $D_{s}^{+} \rightarrow K^{*+} \gamma$ with data collected by the Belle experiment.