In this talk, the potential of linear electron-positron colliders to measure the top quark mass in radiative events is evaluated. A calculation of the differential cross section for production of a top quark pair in association with an energetic photon from initial state radiation, as a function of the center-of-mass energy of the t-tbar system is presented. This matched calculation includes the QCD enhancement of the cross section around the t-tbar production threshold and remains valid in the continuum well above the threshold. The uncertainty in the top mass determination is evaluated in realistic operating scenarios for CLIC and the ILC, including the statistical uncertainty, the theory uncertainty, and dominant experimental systematic uncertainties. With this method, the top quark mass can be determined with a precision of 110 MeV in the initial stage of CLIC, with 1 ab^-1 at 380 GeV and with a precision of approximately 160 MeV at the ILC, with 4 ab^-1 at 500 GeV.