  We introduce a cluster algebraic generalization of Thurston's earthquake map
for the cluster algebras of finite type, which we call the \emph{cluster
earthquake map}. It is defined by gluing exponential maps, which is modeled
after the earthquakes along ideal arcs. We prove an analogue of the earthquake
theorem, which states that the cluster earthquake map gives a homeomorphism
between the spaces of $\mathbb{R}^\mathrm{trop}$- and $\mathbb{R}_{>0}$-valued
points of the cluster $\mathcal{X}$-variety. For those of type $A_n$ and $D_n$,
the cluster earthquake map indeed recovers the earthquake maps for marked disks
and once-punctured marked disks, respectively. Moreover, we investigate certain
asymptotic behaviors of the cluster earthquake map, which give rise to
"continuous deformations" of the Fock--Goncharov fan.
