A technique is presented to measure the efficiency with which c-jets are mistagged as b-jets (mistagging efficiency) using $t\bar{t}$ events, where one of the W bosons decays into an electron or muon and a neutrino and the other decays into a quark–antiquark pair. The measurement utilises the relatively large and known $W\rightarrow cs$ branching ratio, which allows a measurement to be made in an inclusive c-jet sample. The data sample used was collected by the ATLAS detector at $\sqrt{s} = 13$ $\text {TeV}$ and corresponds to an integrated luminosity of 139 fb$^{-1}$. Events are reconstructed using a kinematic likelihood technique which selects the mapping between jets and $t\bar{t}$ decay products that yields the highest likelihood value. The distribution of the b-tagging discriminant for jets from the hadronic W decays in data is compared with that in simulation to extract the mistagging efficiency as a function of jet transverse momentum. The total uncertainties are in the range 3–17%. The measurements generally agree with those in simulation but there are some differences in the region corresponding to the most stringent b-jet tagging requirement.