A search is presented for the single production of vector-like quarks in proton–proton collisions at $$\sqrt{s}=13\,\text {TeV} $$ . The data, corresponding to an integrated luminosity of 35.9 $$\,\text {fb}^{-1}$$ , were recorded with the CMS experiment at the LHC. The analysis focuses on the vector-like quark decay into a top quark and a $$\mathrm {W} $$ boson, with one muon or electron in the final state. The mass of the vector-like quark candidate is reconstructed from hadronic jets, the lepton, and the missing transverse momentum. Methods for the identification of $$\mathrm {b}$$ quarks and of highly Lorentz boosted hadronically decaying top quarks and $$\mathrm {W} $$ bosons are exploited in this search. No significant deviation from the standard model background expectation is observed. Exclusion limits at 95% confidence level are set on the product of the production cross section and branching fraction as a function of the vector-like quark mass, which range from 0.3 to 0.03 $$\,\text {pb}$$ for vector-like quark masses of 700 to 2000 $$\,\text {GeV}$$ . Mass exclusion limits up to 1660 $$\,\text {GeV}$$ are obtained, depending on the vector-like quark type, coupling, and decay width. These represent the most stringent exclusion limits for the single production of vector-like quarks in this channel.