  A particle beam may undergo an anomalous spatial shift when it is reflected
at an interface. The shift forms a vector field defined in the two-dimensional
interface momentum space. We show that, although the shift vector at individual
momentum is typically sensitive to the system details, its integral along a
close loop, i.e., its circulation, could yield a robust quantized number under
certain symmetry conditions of interest. Particularly, this is the case when
the beam is incident from a trivial medium, then the quantized circulation of
anomalous shift (CAS) directly manifests the topological character of the other
medium. We demonstrate that the topological charge of a Weyl medium as well as
the unconventional pair potentials of a superconductor can be captured and
distinguished by CAS. Our work unveils a hidden quantized feature in a
ubiquitous physical process, which may also offer a new approach for probing
topological media.
