The momentum-weighted sum of the charges of tracks associated to a jet is sensitive to the charge of the initiating quark or gluon. This paper presents a measurement of the distribution of momentum-weighted sums, called jet charge, in dijet events using 20.3 fb-1 of data recorded with the ATLAS detector at s=8 TeV in pp collisions at the LHC. The jet charge distribution is unfolded to remove distortions from detector effects and the resulting particle-level distribution is compared with several models. The pT dependence of the jet charge distribution average and standard deviation are compared to predictions obtained with several leading-order and next-to-leading-order parton distribution functions. The data are also compared to different Monte Carlo simulations of QCD dijet production using various settings of the free parameters within these models. The chosen value of the strong coupling constant used to calculate gluon radiation is found to have a significant impact on the predicted jet charge. There is evidence for a pT dependence of the jet charge distribution for a given jet flavor. In agreement with perturbative QCD predictions, the data show that the average jet charge of quark-initiated jets decreases in magnitude as the energy of the jet increases.