A search for the production of a W boson and a Higgs boson through vector boson scattering (VBS) is presented, using CMS data from proton-proton collisions at root s = 13 TeV collected from 2016 to 2018. The integrated luminosity of the data sample is 138 fb(-1). Selected events must be consistent with the presence of two jets originating from VBS, the leptonic decay of the W boson to an electron or muon, possibly also through an intermediate tau lepton, and a Higgs boson decaying into a pair of b quarks, reconstructed as either a single merged jet or two resolved jets. A measurement of the process as predicted by the standard model (SM) is performed alongside a study of beyond-the-SM (BSM) scenarios. The SM analysis sets an observed (expected) 95% confidence level upper limit of 14.3 (9.9) on the ratio of the measured VBS WH cross section to that expected by the SM. The BSM analysis, conducted within the so-called kappa framework, excludes all scenarios with lambda(WZ) < 0 that are consistent with current measurements, where lambda(WZ) = kappa(W)/kappa(Z) and kappa W and kappa(Z) are the HWW and HZZ coupling modfiers, respectively. The significance of the exclusion is beyond 5 standard deviations, and it is consistent with the SM expectation of lambda(WZ) = 1.