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.
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