  In this paper we investigate the existence and uniqueness of weak solutions
for kinetic stochastic differential equations with H\"older diffusion and
unbounded singular drifts in Kato's class. Moreover, we also establish sharp
two-sided estimates for the density of the solution. In particular, the drift
$b$ can be in the mixed $L^q_tL^{p_1}_{x_1}L^{p_2}_{x_2}$ space with
$\frac2q+\frac{d}{p_1}+\frac{3d}{p_2}<1$. As an application, we show the
existence and uniqueness of weak solution to a second order singular
interacting particle system in ${\mathbb R}^{d N}$.
