  The dynamic of string fluctuation under rotating BTZ black hole is studied
using the method of \cite{Son:2009vu}. We compare the result with previous
computation in \cite{Atmaja:2012jg}, with a different method, for the case of
co-rotating string. The result gives definite answer that the end of string
identified as an external quark at the boundary behaves as Brownian particle
with mass is given an effective mass $M_{eff}$ equal to the zero temperature
mass of external quark $M_0$ times Lorentz factor $\gamma$ to the power three.
We also extend the computation for general case of rotating black hole where
the metric is asymptotically $AdS_3$ and the fluctuation is taken only along
the co-rotating motion. It shows that the effective mass of the external quark
is in general given by $\gamma^3 M_0$.
