  We present a calculation of the spin alignment for unflavored vector mesons
in thermalized quark-gluon plasma based on the Kubo formula in linear response
theory. This is achieved by expanding the system to the first order of the
coupling constant and the spatial gradient. The effect strongly relies on the
vector meson's spectral functions which are determined by the interaction and
medium properties. The spectral functions are calculated for the one-quark-loop
self-energy with meson-quark interaction. The numerical results show that the
correction to the spin alignment from the thermal shear tensor is of the order
$10^{-4}\sim10^{-5}$ for the chosen values of quark-meson coupling constant, if
the magnitude of thermal shear tensor is $10^{-2}$.
