  Three-dimensional topological insulators or axion insulators exhibit the
topological magnetoelectric effect, which is isotropic with a universal
coefficient of proportionality quantized in units of $e^2/2h$. Here we study
the finite-size effect of topological magnetoelectric effect, and find the
magnetoelectric coefficients are anisotropic, namely
$\alpha_{xx}\neq\alpha_{zz}$. Both of them are shown to converge to a quantized
value when the thickness of topological insulator film $d$ increases reaching
the three-dimensional bulk limit. The nonzero value of
$(\alpha_{xx}-\alpha_{zz})\propto1/d$ could be measured by using the gyrotropic
or nonreciprocal birefringence of terahertz light. The unique $1/d$ dependence
on film thickness of the rotation angle of optical principle axes is the
manifestation of topological magnetoelectric effect, which may also serve as a
smoking gun signature for axion insulators.
