  We study the spin alignment of neutral rho mesons in a pion gas using spin
kinetic or Boltzmann equations. The $\rho\pi\pi$ coupling is given by the
chiral effective theory. The collision terms at the leading and next-to-leading
order in spin Boltzmann equations are derived. The evolution of the spin
density matrix of the neutral rho meson is simulated with different initial
conditions. The numerical results show that the interaction of pions and
neutral rho mesons creates very small spin alignment in the central rapidity
region if there is no rho meson in the system at the initial time. Such a small
spin alignment in the central rapidity region will decay rapidly toward zero in
later time. If there are rho mesons with a sizable spin alignment at the
initial time the spin alignment will also decrease rapidly. We also considered
the effect on $\rho_{00}$ from the elliptic flow of pions in the blast wave
model. With vanishing spin alignment at the initial time, the deviation of
$\rho_{00}$ from 1/3 is positive but very small.
