We theoretically investigate a possibility of an $eta ^{prime} d$ bound state and its formation in the $gamma d to eta d$ reaction. First, in the fixed center approximation to the Faddeev equations we obtain an $eta ^{prime} d$ bound state with a binding energy of 25 MeV and width of 19 MeV, where we take the $eta ^{prime} N$ interaction with a coupling to the $eta N$ channel from the linear $sigma$ model. Then, in order to investigate the feasibility from an experimental point of view, we calculate the cross section of the $gamma d to eta d$ reaction at the photon energy in the laboratory frame around 1.2 GeV. As a result, we find a clear peak structure with the strength $sim$ 0.2 nb/sr, corresponding to a signal of the $eta ^{prime} d$ bound state in case of backward $eta$ emission. This structure will be prominent because a background contribution coming from single-step $eta$ emission off a bound nucleon is highly suppressed. In addition, the signal can be seen even in case of forward $eta$ emission as a bump or dip, depending on the relative phase between the bound-state formation and the single-step background.
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