A search is performed for the rare decay $\mathrm{W^{\pm}}\to\pi\gamma$ in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$. Data corresponding to an integrated luminosity of $137~\mathrm{fb^{-1}}$ were collected during 2016 to 2018 with the CMS detector. This analysis exploits a novel search strategy based on W boson production in top quark pair events. An inclusive search for the $\mathrm{W^{\pm}}\to\pi\gamma$ decay is not optimal at the LHC because of the high trigger thresholds. Instead, a trigger selection is exploited in which the W boson originating from one of the top quarks is used to tag the event in a leptonic decay. The W boson emerging from the other top quark is used to search for the $\mathrm{W^{\pm}}\to\pi\gamma$ signature. Such decays are characterized by an isolated track pointing to a large energy deposit, and by an isolated photon of large transverse momentum. The presence of b quark jets reduces the background from the hadronization of light-flavor quarks and gluons. The $\mathrm{W^{\pm}}\to\pi\gamma$ decay is not observed. An upper exclusion limit is set to this branching fraction, corresponding to $1.50\times 10^{-5}$ at $95\%$ confidence level, whereas the expected upper exclusion limit is $0.85^{+0.52}_{-0.29} \times 10^{-5}$.