  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 $\sqrt{s}$ = 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, 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 (9.0) 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 $\lambda_\mathrm{WZ}$ $\lt$ 0 that are consistent with current
measurements, where $\lambda_\mathrm{WZ}$ =
$\kappa_\mathrm{W}/\kappa_\mathrm{Z}$ and $\kappa_\mathrm{W}$ and
$\kappa_\mathrm{Z}$ are the HWW and HZZ coupling modifiers, respectively. The
signficance of the exclusion is beyond 5 standard deviations, and it is
consistent with the SM expectation of $\lambda_\mathrm{WZ}$ = 1.
