  We study the real part of the static potential of a heavy quark-antiquark
system in an anisotropic plasma medium. We use a quasi-particle approach where
the collective dynamics of the plasma constituents is described using hard-loop
perturbation theory. The parton distribution function is characterized by a set
of parameters that can accurately describe the anisotropy of the plasma
produced in a heavy ion collision. We calculate the potential numerically in
strongly anisotropic systems and study the angular dependence of the distortion
of the potential relative to the isotropic one. We obtain an analytic
expression for the real part of the heavy quark potential in the limit of weak
anisotropy using a model that expresses the potential in terms of effective
screening masses that depend on the anisotropy parameters and the orientation
of the quark-antiquark pair. A 1-dimensional potential is formulated in terms
of angle averaged screening masses that incorporate the anisotropy of the
medium into a radial coordinate. We solve the corresponding Schr\"odinger
equation and show that the magnitude of the binding energy typically increases
with anisotropy. Anisotropy can play an important role, especially in states
with non-zero angular momentum. This means that the number of bound states that
are formed could depend on specific characteristics of the anisotropy of the
plasma. Our study suggests that plasma anisotropy plays an important role in
the dynamics of heavy quarkonium and motivates further study.
