  The axion is a hypothetical but experimentally undetected particle. Recently,
the antiferromagnetic topological insulator MnBi$_2$Te$_4$ has been predicted
to host the axion insulator, but the experimental evidence remains elusive.
Specifically, the axion insulator is believed to carry "half-quantized" chiral
currents running antiparallel on its top and bottom surfaces. However, it is
challenging to measure precisely the half-quantization. Here, we propose a
nonlocal surface transport device, in which the axion insulator can be
distinguished from normal insulators without a precise measurement of the
half-quantization. More importantly, we show that the nonlocal surface
transport, as a qualitative measurement, is robust in realistic situations when
the gapless side surfaces and disorder come to play. Moreover, thick electrodes
can be used in the device of MnBi$_2$Te$_4$ thick films, enhancing the
feasibility of the surface measurements. This proposal will be insightful for
the search of the axion insulator and axion in topological matter.
