A measurement is presented for the electroweak production of a W boson, a photon (γ), and two jets (j) in proton-proton collisions. The leptonic decay of the W boson is selected by requiring one identified electron or muon and large missing transverse momentum. The two jets are required to have large invariant dijet mass and large separation in pseudorapidity. The measurement is performed with the data collected by the CMS detector at a center-of-mass energy of 13  TeV, corresponding to an integrated luminosity of 138  fb⁻¹. The cross section for the electroweak Wγjj production is 23.5^+4.9_−4.7  fb, whereas the total cross section for Wγjj production is 113±13  fb. Differential cross sections are also measured with the distributions unfolded to the particle level. All results are in agreement with the standard model expectations. Constraints are placed on anomalous quartic gauge couplings (aQGCs) in terms of dimension-8 effective field theory operators. These are the most stringent limits to date on the aQGCs parameters f_M,2–5/Λ⁴ and f_T,6–7/Λ⁴.