  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.
