  When a D-brane wraps around a cycle of a curved manifold, the twisting of its
normal bundle can induce chiral asymmetry in its worldvolume theory. We obtain
the general form of the resulting anomalies for D-branes and their
intersections. They are not cancelled among themselves, and the standard inflow
mechanism does not apply at first sight because of their apparent lack of
factorizability and the apparent vanishing of the corresponding inflow. We show
however after taking into consideration the effects of the nontrivial topology
of the normal bundles, the anomalies can be transformed into factorized forms
and precisely cancelled by finite inflow from the Chern-Simons actions for the
D-branes as long as the latter are well defined. We then consider examples in
type II compactifications where the twisting of the normal bundles occurs and
calculate the changes in the induced Ramond-Ramond charges on the D-branes.
