  The elliptic flows of thermal di-electrons are investigated within a
(2+1)-dimension event-by-event hydrodynamic model for Au+Au collisions at
$\sqrt{s_{NN}}=200$ GeV. The fluctuating initial conditions are given by the
Monte Carlo Glauber model. We find in our event-by-event calculation rather
weak correlation between the dilepton emission angles and the event plane
angles of charged hadrons. We observe strong fluctuation effects in dilepton
elliptic flows when using the event plane angles of dileptons at specific
invariant mass $M$. The correlation between the dilepton event plane angle and
charged hadron one becomes stronger with decreasing $M$. This provides a
possible measure of the interplay between the effect of geometric deformation
and that of fluctuating "hot spots" in relativistic heavy ion collisions.
