The non-perturbative QCD effects involved in radiative tau decay ($\tau^- \rightarrow \pi^- \nu_\tau \gamma$) are encoded in two form factors (FFs); vector ($F_V$) and axial-vector ($F_A$). These FFs are the same as those involved in radiative pion decay with the crucial difference that the square of the momentum transferred, $t$, between the $\pi-\gamma$ system is positive. This makes them timelike and can result in the production of real hadronic resonances. We calculate the analytical form for these FFs using the method of light-cone sum rules (LCSR) and present the decay width and the invariant mass spectrum of the $\pi-\gamma$ system. The structure-dependent parameter $\gamma$ (i.e., $\frac{F_A}{F_V}$ at zero momentum transfer) is found to be in good agreement with the experimental determination.