Recently, nonreciprocal two-dimensional unitary scattering networks have gained considerable interest due to the possibility of obtaining robust edge wave propagation in their anomalous topological insulating phase. However, zero-dimensional states in such networks have been left uncharted. Here, we demonstrate the existence of disclination states in nonreciprocal topological scattering networks. The disclination states can nucleate in every gap of the anomalous phase if a disclination round-trip resonance condition is met, and are carried over to the Chern phase unless the band gap closes. By comparing Chern and anomalous disclination states, we show that only the latter are remarkably robust to random quasienergy fluctuations. Anomalous topological chiral edge states and disclinations can be coupled together to form intriguing disclination bound states in the continuum (BICs) in anomalous topological insulators, a different form of nonreciprocal cavities associated with an extreme confinement and lifetime. Our work broadens the applications of disclination states to microwave, acoustic, or optical scattering networks, with new possibilities in chiral topological lasing, robust nonreciprocal energy squeezing, and switchable lasing and antilasing behavior.