In this paper we address the potential of a 3 TeV center-of-mass energy Compact Linear Collider (CLIC) to measure the branching fraction of the Higgs boson decay to two photons, $\mathrm{BR}(H\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})$. Since photons are massless, the Higgs boson coupling to photons is realized through higher order processes involving heavy particles either from the Standard Model or beyond. Any deviation of the measured $\mathrm{BR}(H\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})$, and consequently of the Higgs coupling ${g}_{H\ensuremath{\gamma}\ensuremath{\gamma}}$ from the predictions of the Standard Model, may indicate new physics. The Higgs decay to two photons is thus an interesting probe of the Higgs sector. This study is performed using the simulation of the detector for CLIC and by considering all relevant physics and beam-induced processes in a full reconstruction chain. It is shown that the product of the Higgs production cross section in ${W}^{+}{W}^{\ensuremath{-}}$ fusion and $\mathrm{BR}(H\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})$ can be measured with a relative statistical uncertainty of 5.5%, assuming the integrated luminosity of $5\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ and unpolarized beams.