  Using the dilute-dense factorization in the Color Glass Condensate framework,
we investigate the azimuthal angular correlation between a heavy quarkonium and
a charged light hadron in proton-nucleus collisions. We extract the second
harmonic $v_2$, commonly known as the elliptic flow, with the light hadron as
the reference. This particular azimuthal angular correlation between a heavy
meson and a light hadron has first been measured at the LHC recently. The
experimental results indicate that the elliptic flows for heavy-flavor mesons
($J/\psi$ and $D^0$) are almost as large as those for light hadrons. Our
calculation demonstrates that this result can be naturally interpreted as an
initial state effect due to the interaction between the incoming partons from
the proton and the dense gluons inside the target nucleus. Since the heavy
quarkonium $v_2$ exhibits a weak mass dependence according to our calculation,
we predict that the heavy quarkonium $\Upsilon$ should have a similar elliptic
flow as compared to that of the $J/\psi$, which can be tested in future
measurements.
