  We examine pinning and dynamics of Abrikosov vortices interacting with
pinning centers placed in a moir\'e pattern for varied moir\'e lattice angles.
We find a series of magic angles at which the critical current shows a
pronounced dip corresponding to lattices in which the vortices can flow along
quasi-one-dimensional channels. At these magic angles, the vortices move with a
finite Hall angle. Additionally, for some lattice angles there are peaks in the
critical current produced when the substrate has a quasiperiodic character that
strongly reduces the vortex channeling. Our results should be general to a
broad class of particle-like assemblies moving on moir\'e patterns.
