The cross-section of top-quark-antiquark pair production in association with a photon is important in order to determine the electromagnetic coupling of the top-quark with high precision. It is also of great significance to test deviations from the Standard Model, such as anomalous dipole moments of the top-quark. Furthermore, such cross-section can be interpreted in effective field theories which would allow for probing effects of higher-dimensional operators of the Standard Model fields. The inclusive and differential cross-sections of top-quark production in association with a photon in the electron-muon channel at $\sqrt{s} = 13~\text{TeV}$ with the ATLAS detector at the LHC are measured. The measurements are performed in a fiducial volume. The fiducial inclusive cross-section is extracted using a profile likelihood fit, while the fiducial differential cross-section is measured at parton level as a function of various observables, such as the photon transverse momentum and angular variables related to the photon and the leptons. The measurements are compared to the most recent next-to-leading-order theory calculation and state-of-the-art Monte Carlo simulations. The results are found to be in good agreement with the predictions within uncertainties.