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We obtain bounds on the anomalous magnetic and electric dipole moments of the t-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 processes γe-→t¯bνe (γ is the Compton backscattering photon) and e+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 of δsys=0%  (5%), b-tagging  efficiency=0.8, center-of-mass energy of s=3 TeV, and integrated luminosity of L=2ab-1 the future e+e- collider may put bounds on the electromagnetic dipole moments a^V and a^A of the top quark of the order of O(10-2–10-1) at the 2σ  (3σ) level, which are competitive with those recently reported in previous studies at hadron colliders and the ILC.