  We theoretically analyze the energy spectrum of a quantum ring in AA-stacked
bilayer graphene with radius $R$ for a zero width subjected to a perpendicular
magnetic field $B$. An analytical approach, using the Dirac equation, is
implemented to obtain the energy spectrum by freezing out the carrier radial
motion. The obtained spectrum exhibits different symmetries and for a fixed
total angular momentum $m$, it has a hyperbolic dependence of the magnetic
field. In particular, the energy spectra are not invariant under the
transformation $B \longrightarrow -B$. The application of a potential, on the
upper and lower layer, allows to open a gap in the energy spectrum and the
application of a non zero magnetic field breaks all symmetries. We also analyze
the basics features of the energy spectrum to show the main similarities and
differences with respect to ideal quantum ring in monolayer, AB-stacked bilayer
graphene and a quantum ring with finite width in AB-stacked bilayer graphene.
