  Vortices in chiral topological superconductors are known for trapping
Majorana zero modes as a signature response to their bulk-state topologies. In
this work, we establish a similar bulk-vortex correspondence for
two-dimensional $C_n$-protected class D higher-order topological
superconductors, in which a quantum vortex will universally trap a pair of
$C_n$-protected Majorana bound states with $\hat{z}$-directional angular
momenta $J_z=0$ and $J_z=n/2$, respectively. This intriguing one-to-one mapping
between anomalous vortex modes and higher-order topology can be systematically
derived through a model-independent patch construction approach. As a proof of
concept, we present an exactly solvable model to confirm the proposed vortex
Majorana modes. Our theory establishes vortices as an unprecedented
experimental measure of higher-order topology in superconductors.
