  The vector boson scattering at the Large Hadron Collider (LHC) is sensitive
to anomalous quartic gauge couplings (aQGCs). In this paper, we investigate the
aQGC contribution to $ W \gamma jj$ production at the LHC with $\sqrt{s}=13$
TeV in the context of an effective field theory (EFT). The unitarity bound is
applied as a cut on the energy scale of this production process, which is found
to have significant suppressive effects on the signals. To enhance the
statistical significance, we analyse the kinematic and polarization features of
the aQGC signals in detail. We find that the polarization effects induced by
the aQGCs are unique and can discriminate the signals from the SM backgrounds
well. With the proposed event selection strategy, we obtain the constraints on
the coefficients of dimension-8 operators with current luminosity. The results
indicate that the process $pp \to W \gamma jj$ is powerful for searching for
the $O_{M_{2,3,4,5}}$ and $O_{T_{5,6,7}}$ operators.
