Measurements of jet substructure are key to probing the energy frontier at colliders, and many of them use track-based observables which take advantage of the angular precision of tracking detectors. Theoretical calculations of track-based observables require ‘track functions’, which characterize the transverse momentum fraction rq carried by charged hadrons from a fragmenting quark or gluon. This letter presents a direct measurement of rq distributions in dijet events from the 140 fb⁻¹ of proton–proton collisions at s=13 TeV recorded with the ATLAS detector. The data are corrected for detector effects using machine-learning methods. The scale evolution of the moments of the rq distribution is sensitive to non-linear renormalization group evolution equations of QCD, and is compared with analytic predictions. When incorporated into future theoretical calculations, these results will enable a precision program of theory-data comparison for track-based jet substructure observables.