  By using the AdS/CFT correspondence and G\"{o}del black hole background, we
study the dynamics of heavy quark under a rotating plasma. In that case we
follow Atmaja (JHEP 1304, 021, (2013)) about Brownian motion in BTZ black hole.
In this paper we receive some new results for the case of
$\alpha^{2}l^{2}\neq1$. This case, we must redefine the angular velocity of
string fluctuation. We obtain the time evolution of displacement square that
angular velocity and show that it behaves as a Brownian particle in
non-relativistic limit. In this plasma, it seems that relating the Brownian
motion with physical observables is rather a difficult work. But our results
match with Atmaja work in the limit $\alpha^{2}l^{2}\rightarrow1$.
