  In this paper, we investigate the $\rm \gamma p$ photoproduction of jet plus
missing energy signal to set limits on the couplings of the fermionic dark
matter to the quarks at the LHC via the main reaction $\rm pp\rightarrow
p\gamma p\rightarrow p \chi\chi j$. We assume a typical LHC multipurpose
forward detectors and work in a model independent Effective Field Theory
framework. Typically, when we do the background analysis, we also include their
corresponding Single Diffractive (SD) productions. Our result shows that by
requiring a $5\sigma$ ($\rm S/\sqrt{B} \geq 5$) signal deviation, with an
integrated luminosity of $\rm {\cal L} = 200 fb^{-1}$, the lower bounds of WIMP
masses scale can be detected up to $\rm \Lambda$ equal 665.5, 808.9 and 564.0
GeV for the forward detector acceptances $\xi_1$, $\xi_2$, and $\xi_3$,
respectively, where $0.0015<\xi_1<0.5$, $0.1<\xi_2<0.5$ and
$0.0015<\xi_3<0.15$.
