Quantum Chromodynamics (QCD), the theory of the strong interaction between quarks and gluons, predicts that at extreme conditions of high temperature and/or density, quarks and gluons are no longer confined within individual hadrons. This new deconfined state of quarks and gluons is called Quark-Gluon Plasma (QGP). The Universe was in this QGP state a few microseconds after the Big Bang. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) on Long Island, NY was built to create and study the properties of QGP.Due to their heavy masses, quarks with heavy flavor (charm and bottom) are mainly created during the early, energetic stages of the collisions. Heavy flavor is considered to be a unique probe for QGP studies, since it propagates through all phases of a collision, and is affected by the hot and dense medium throughout its evolution. Initial studies, via indirect reconstruction of heavy flavor using their decay electrons, indicated a much higher energy loss by these quarks compared to model predictions, with a magnitude comparable to that of light quarks. Mesons such as D0 could provide information about the interaction of heavy quarks with the surrounding medium through measurements such as elliptic flow. Such data help constrain the transport parameters of the QGP medium and reveal its degree of thermalization.Because heavy hadrons have a low production yield and short lifetime (e.g. ct = 120μm for D0), it is very challenging to obtain accurate measurements of open heavy flavor in heavy-ion collisions, especially since the collisions also produce large quantities of light-flavor particles. Also due to their short lifetime, it is difficult to distinguish heavy-flavor decay vertices from the primary collision vertex; one needs a very high precision vertex detector in order to separate and reconstruct the decay of the heavy flavor particles in the presence of thousands of other particles produced in each collision.The STAR collaboration built a new micro-vertex detector and installed it in the experiment in 2014. This state-of-the-art silicon pixel technology is named the Heavy Flavor Tracker (HFT). The HFT was designed in order to perform direct topological reconstruction of the weak decay products from hadrons that include a heavy quark. The HFT consists of four layers of silicon, and it improves the track pointing resolution of the STAR experiment from a few mm to around 30 ℗æm for charged pions at a momentum of 1 GeV/c.In this dissertation, I focus on one of the main goals of the HFT detector, which is to study the elliptic flow v2 (a type of azimuthal anisotropy) for D0 mesons in Au+Au collisions at vsNN = 200 GeV. My analysis is based on the 2014 data set (about 1.2 billion collisions covering all impact parameters) that include data from the HFT detector. There are two new and unique analysis elements used in this dissertation. First, I performed the analysis using a Kalman filter algorithm to reconstruct the charmed-meson candidates. The standard reconstruction is via a simple helix-swim method. The advantage of using the Kalman algorithm is in the use of the full error matrix of each track in the vertex estimation and reconstruction of the properties of the heavy-flavor parent particle. Second, I also used the Tool for Multivariate Analysis (TMVA), a ROOT-environment tool, to its full potential for signal significance optimization, instead of the previous approach based on a set of fixed cuts for separating signal from background.This dissertation presents the elliptic component (v2) of azimuthal anisotropy of D0 mesons as a function of transverse momentum, pT . The centrality (impact parameter) dependence of D0 v2(pT) is also studied. Results are compared with similar studies involving light quarks, and with the predictions of several theoretical models.