We study the kinetic Kuramoto model for coupled oscillators. We prove
that for any regular free state, if the interaction is small enough, it exists a solution which
converges to it. For this class of solution the order parameter vanishes to zero, showing
a behavior similar to the phenomenon of Landau damping in plasma physics. We obtain
an exponential decay of the order parameter in the case on analytical regularity of the
asymptotic state, and a polynomial decay in the case of Sobolev regularity.