  A search for W$\gamma$ resonances in the mass range between 0.7 and 6.0 TeV
is presented. The W boson is reconstructed via its hadronic decays, with the
final-state products forming a single large-radius jet, owing to a high Lorentz
boost of the W boson. The search is based on proton-proton collision data at
$\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 137
fb$^{-1}$, collected with the CMS detector at the LHC in 2016-2018. The
W$\gamma$ mass spectrum is parameterized with a smoothly falling background
function and examined for the presence of resonance-like signals. No
significant excess above the predicted background is observed. Model-specific
upper limits at 95% confidence level on the product of the cross section and
branching fraction to the W$\gamma$ channel are set. Limits for narrow
resonances and for resonances with an intrinsic width equal to 5% of their
mass, for spin-0 and spin-1 hypotheses, range between 0.17 fb at 6.0 TeV and 55
fb at 0.7 TeV. These are the most restrictive limits to date on the existence
of such resonances over a large range of probed masses. In specific heavy
scalar (vector) triplet benchmark models, narrow resonances with masses between
0.75 (1.15) and 1.40 (1.36) TeV are excluded for a range of model parameters.
Model-independent limits on the product of the cross section, signal
acceptance, and branching fraction to the W$\gamma$ channel are set for minimum
W$\gamma$ mass thresholds between 1.5 and 8.0 TeV.
