  Charmonium directed flows are studied based on transport model coupled with
the realistic three dimensional expansions of the bulk medium. The non-central
symmetric nucleus-nucleus collisions can generate the rotating quark-gluon
plasma (QGP) with symmetry-breaking longitudinal distributions. In
$\sqrt{s_{NN}}=200$ GeV Au-Au semi-central collisions, charmonium are
primordially produced in the initial hard process, they are mainly dissociated
by the initial tilted source with high temperatures and then move out of the
bulk medium to keep the early information of the medium. Charmonia are less
affected by the hydrodynamic expansions of QGP where its tilted shape is being
diluted. This biased dissociation can generate directed flows of $J/\psi$ and
$\psi(2S)$ which are much larger than the values of light charged hadrons and
open heavy flavor. They are sensitive and clean to the effect of QGP
rapidity-odd initial energy densities.
