  The quantum Hall effect is usually observed in 2D systems. We show that the
Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological
semimetals. Because of the topological constraint, the Fermi arc at a single
surface has an open Fermi surface, which cannot host the quantum Hall effect.
Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at
opposite surfaces can form a complete Fermi loop and support the quantum Hall
effect. The edge states of the Fermi arcs show a unique 3D distribution, giving
an example of (d-2)-dimensional boundary states. This is distinctly different
from the surface-state quantum Hall effect from a single surface of topological
insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall
conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl
nodes. This behavior can be realized by tuning gate voltages in a slab of
topological semimetal, such as the TaAs family, Cd$_3$As$_2$, or Na$_3$Bi. This
work will be instructive not only for searching transport signatures of the
Fermi arcs but also for exploring novel electron gases in other topological
phases of matter.
