  Rotating neutron star or pulsar can be a possible source of pseudo Nambu
Goldstone bosons or axions which can mediate long range axionic hair outside of
the pulsar. When the electromagnetic radiation is emitted from pulsar and
passes through the long range axion hair, the axion rotates the polarization of
the electromagnetic radiation and produces birefringence. We obtain the angle
of birefringence due to this long range axionic hair as $0.42^\circ$. This
result is independent of the rotational frequency, radius of the pulsar, mass
of the axion, and axion photon coupling constant. This value is within the
accuracy of measuring the linear polarization angle of pulsar light which is
$\leq 1.0^\circ$. Our result continues to hold as long as the range of the
axion hair (inverse of axion mass) is greater than the radius of the pulsar,
i.e; $m_a<10^{-11}$eV and the axion decay constant $f_a\lesssim
\mathcal{O}(10^{17}\rm{GeV})$.
