  High energy proton-nucleus (pA) collisions provide an important constraint on
the study of the chiral magnetic effect in QCD matter. Naively, in pA
collisions one expects no correlation between the orientation of event plane as
reconstructed from the azimuthal distribution of produced hadrons and the
orientation of magnetic field. If this is the case, any charge-dependent hadron
correlations can only result from the background. Nevertheless, in this paper
we point out that in high multiplicity pA collisions a correlation between the
magnetic field and the event plane can appear. This is because triggering on
the high hadron multiplicity amounts to selecting Fock components of the
incident proton with a large number of partons that are expected to have a
transverse size much larger than the average proton size. We introduce the
effect of the fluctuating proton size in the Monte Carlo Glauber model and
evaluate the resulting correlation between the magnetic field and the
second-order event plane in both pA and nucleus-nucleus (AA) collisions. The
fluctuating proton size is found to result in a significant correlation between
magnetic field and the event plane in pA collisions, even though the magnitude
of the correlation is still much smaller than in AA collisions. This result
opens a possibility of studying the chiral magnetic effect in small systems.
