  We investigate the possibility of charged pion condensation in the presence
of parallel rotation and magnetic field within the Nambu--Jona-Lasinio model
with quarks as the fundamental degrees of freedom. Previous study based on
non-interacting Klein-Gordon theory for pions showed that the charged pions
will undergo Bose-Einstein condensation under this circumstance [Y. Liu and I.
Zahed, Phys. Rev. Lett. ${\bf 120}$, 032001 (2018)]. In this work, we take into
account the internal quark structures of charged pions self-consistently
through quark polarization loops in an interacting theory, i.e., the
Nambu--Jona-Lasino model. The stability of the system is explored against the
formation of a nonzero expectation value of the composite charged pion field
$\bar{u}i\gamma_5d$. We find that two competing effects are induced by the
rotation: the isospin enhancement which favors charged pion condensation and
the spin breaking which disfavors the condensation. For a strong magnetic field
($\sqrt{eB}\sim1{\rm GeV}$) and system size of a few fermi, the isospin
enhancement effect is stronger than the spin breaking one, and the charged pion
condensation becomes energetically favored beyond a critical angular velocity
of a few MeV.
