Radial superlattices are nanostructured materials obtained by rolling up thin solid films into spiral-like tubular structures. The formation of these "high-order" superlattices from two-dimensional crystals or ultrathin films is expected to result in a transition of transport characteristics from two-dimensional to one-dimensional. Here, we show that a transport hallmark of radial superlattices is the appearance of magnetoconductance modulations in the presence of externally applied axial magnetic fields. This phenomenon critically relies on electronic interlayer tunneling processes that activate an unconventional Aharonov-Bohm-like effect. Using a combination of density functional theory calculations and low-energy continuum models, we determine the electronic states of a paradigmatic single-material radial superlattice - a two-winding carbon nanoscroll - and indeed show momentum-dependent oscillations of the magnetic states in the axial configuration, which we demonstrate to be entirely due to hopping between the two windings of the spiral-shaped scroll.