We present the full O(alpha) electroweak radiative corrections to the process e(+) e(-) -> t (t) over bar 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 (AFB) as a function of the center-of-mass energy and compare them with the process e(+) e(-) -> t (t) over bar. We find that the value of AFB in t (t) over bar gamma production is larger than AFB in t (t) over bar 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 a scheme and the G(mu) scheme (delta(G mu)(W)). We obtain numerical values for delta(G mu)(W) which are changing from 2 % to -24 % when we vary the center-of-mass energy from 360 GeV to 1 TeV.