  We investigate contributions of Kaluza-Klein (KK) graviton in extra dimension
models to the process $pp \to p\gamma p \to p\gamma j X$, where a proton emits
a quasireal photon and is detected by using the very forward detectors planned
at the LHC. In addition to the $\gamma q$ initial state as in the Compton
scattering in the standard model, the $\gamma g$ scattering contributes through
the $t$-channel exchange of KK gravitons. Taking account of pileup
contributions to the background and examining viable kinematical cuts,
constraints on the parameter space of both the ADD (Arkani-Hamed, Dimopoulos
and Dvali) model and the RS (Randall and Sundrum) model are studied. With 200
fb$^{-1}$ data at a center-of-mass energy of 14 TeV, the expected lower bound
on the cut-off scale for the ADD model is 6.3 TeV at 95% confidence level,
while a lower limit of 2.0 (0.5) TeV is set on the mass of the first excited
graviton with the coupling parameter $k/\overline{M}_{\rm Pl}=0.1$ (0.01) for
the RS model.
