  In the presence of crystalline symmetries, certain topological insulators
present a filling anomaly: a mismatch between the number of electrons in an
energy band and the number of electrons required for charge neutrality. In this
paper, we show that a filling anomaly can arise when corners are introduced in
$C_n$-symmetric crystalline insulators with vanishing polarization, having as
consequence the existence of corner-localized charges quantized in multiples of
$\frac{e}{n}$. We characterize the existence of this charge systematically and
build topological indices that relate the symmetry representations of the
occupied energy bands of a crystal to the quanta of fractional charge robustly
localized at its corners. When an additional chiral symmetry is present,
$\frac{e}{2}$ corner charges are accompanied by zero-energy corner-localized
states. We show the application of our indices in a number of atomic and
fragile topological insulators and discuss the role of fractional charges bound
to disclinations as bulk probes for these crystalline phases.
