The cross-section of top-quark pair production in association with a photon in proton-proton collisions at a center of mass energy of $\sqrt{s} = 8~\mathrm{TeV}$ is measured. The data with a total integrated luminosity of $20.2~\mathrm{fb}^{-1}$ collected by the ATLAS detector in 2012 is used. The measurement is performed in the single lepton decay channel. The signal region is defined by the final state of exactly one high $p_{\mathrm{T}}$ lepton, large missing transverse momentum, at least four jets where at least one is being $b$-tagged and exactly one photon with $p_{\mathrm{T}} > 15~\mathrm{GeV}$. The cross-section times the branching ratio is determined in a fiducial region defined in terms of the detector acceptance. In addition, the first differential cross-section measurements as a function of photon $p_{\mathrm{T}}$ and $\eta$ are presented. The measured fiducial inclusive and differential cross sections are in good agreement with the NLO prediction.