This Letter reports the observation of single top quarks produced together with a photon, which directly probes the electroweak coupling of the top quark. The analysis uses 139 fb^{-1} of 13 TeV proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider. Requiring a photon with transverse momentum larger than 20 GeV and within the detector acceptance, the fiducial cross section is measured to be 688±23(stat) _{-71}^{+75}(syst) fb, to be compared with the standard model prediction of 515_{-42}^{+36} fb at next-to-leading order in QCD.