A search for the electroweak production of a vector-like quark T, decaying to a top quark and a Higgs boson is presented. The search is based on a sample of proton-proton collision events recorded at the LHC at root s = 13 TeV, corresponding to an integrated luminosity of 138 fb(-1). This is the first T ' search that exploits the Higgs boson decay to a pair of photons. For narrow isospin singlet T ' states with masses up to 1.1 TeV, the excellent diphoton invariant mass resolution of 1-2% results in an increased sensitivity compared to previous searches based on the same production mechanism. The electroweak production of a T ' quark with mass up to 960 GeV is excluded at 95% confidence level, assuming a coupling strength kappa(T) = 0.25 and a relative decay width Gamma/M-T '< 5%.