A search is conducted for a low-mass charged Higgs boson produced in a top quark decay and subsequently decaying into a charm and a strange quark. The data sample was recorded in proton-proton collisions at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ by the CMS experiment at the LHC and corresponds to an integrated luminosity of $35.9\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. The search is performed in the process of top quark pair production, where one top quark decays to a bottom quark and a charged Higgs boson and the other to a bottom quark and a $W$ boson. With the $W$ boson decaying to a charged lepton (electron or muon) and a neutrino, the final state comprises an isolated lepton, missing transverse momentum, and at least four jets, of which two are tagged as $b$ jets. To enhance the search sensitivity, one of the jets originating from the charged Higgs boson is required to satisfy a charm tagging selection. No significant excess beyond standard model predictions is found in the dijet invariant mass distribution. An upper limit in the range 1.68%--0.25% is set on the branching fraction of the top quark decay to the charged Higgs boson and bottom quark for a charged Higgs boson mass between 80 and 160 GeV.