We establish model-independent sensitivity on the anomalous magnetic and electric dipole moments of the τ-lepton using the two-photon processes γγ → τ þ τ − and γγ → τ þ τ − γ. We use L ¼ 10, 50, 100, 300, 500, 1000, 1500, 2000, 3000 fb −1 data collected with the future e þ e − linear collider such as the CLIC at ffiffi ffi s p ¼ 380, 1500, 3000 GeV, and we consider systematic uncertainties of δ sys ¼ 0%, 3%, 5%. We obtain sensitivity estimates at 95% C.L. on the anomalous dipole moments to the τ-lepton −0.00015 ≤ã τ ≤ 0.00017 and jd τ ðecmÞj ¼ 9.040 × 10 −19 that may be achievable in future experiments. Our results show that the processes under consideration are very promising for probing the dipole moments of the τ-lepton at the future e þ e − linear collider at the γγ mode.