  We consider the three-dimensional rotating motions of neutron stars blown by
the "axion wind". Neutron star precession and spin can change from the magnetic
moment coupling to the oscillating axion background field, in analogy to the
gyroscope motions with a driving force and the laboratory Nuclear Magnetic
Resonance(NMR) detections of the axion. This effect modulates the pulse arrival
time of the pulsar timing arrays. It shows up as a signal on the timing
residual and two-point correlation function on the recent data of Nanograv and
PPTA. The current measurement of PTAs can thus cast constraints on the
axion-nucleon coupling as g_{ann} ~ 10^{-12}{GeV}^{-1}.
