The Compact Linear Collider (CLIC) is one of the most popular linear colliders, planned to realize e(-)e(+) collisions in three energy stages of 0.5, 1.5 and 3 TeV. It has an energy scale never reached by any existing lepton collider. In this study, we present the sensitivity studies of the WW gamma gamma anomalous quartic gauge boson coupling (aQGC) in the three different processes e(+)e(-) -> W-W+gamma, e(+)e(-) -> e(+) gamma*e(-) -> e(+) W-gamma nu(e) and e(+)e(-) -> e(+) gamma*gamma*e- -> e(+)W(-)W(+)e-at the CLIC. We obtained 95% confidence level limits on the aQGC parameters a(0)/Lambda(2) and a(c) /Lambda(2) at various integrated luminosities and centerof- mass energies. The best limits obtained on the aQGCs a(0)/Lambda(2) and a(c) /Lambda(2) in these processes are at the order of 10(-2) TeV-2 and 10(-1) TeV-2, respectively.