We obtain bounds on the anomalous magnetic and electric dipole moments of thet-quark from a future high-energy and high-luminosity linear electron positron collider, as the CLIC, with polarized and unpolarized electron beams which are powerful tools for determining new physics. We consider the processesγe-→t¯bνe(γis the Compton backscattering photon) ande+e-→e-γ⁎e+→t¯bνee+(γ⁎is the Weizsacker-Williams photon) as they are one of the most important sources of single top quark production. For systematic uncertainties ofδsys=0% (5%),b-tagging efficiency=0.8, center-of-mass energy ofs=3 TeV, and integrated luminosity ofL=2ab-1the futuree+e-collider may put bounds on the electromagnetic dipole momentsa^Vanda^Aof the top quark of the order ofO(10-2–10-1)at the2σ (3σ)level, which are competitive with those recently reported in previous studies at hadron colliders and the ILC.