We present the full \(\mathcal{O}(\alpha)\) electroweak radiative corrections to the process \(e^{+}e^{-} \rightarrow t \bar{t} \gamma\) at the International Linear Collider (ILC). The computation is performed with the help of the GRACE-Loop system. We present the total cross-section and the top quark forward–backward asymmetry (A FB) as a function of the center-of-mass energy and compare them with the process \(e^{+}e^{-} \rightarrow t \bar{t}\). We find that the value of A FB in \(t \bar{t} \gamma\) production is larger than A FB in \(t\bar{t}\) production. It is an important result for the measurement of the top quark forward–backward asymmetry at the ILC. Applying a structure function method, we also subtract the QED correction to gain the genuine weak correction in both the α scheme and the G μ scheme (\(\delta_{W}^{G_{\mu}}\)). We obtain numerical values for \(\delta_{W}^{G_{\mu}}\) which are changing from 2 % to −24 % when we vary the center-of-mass energy from 360 GeV to 1 TeV.