Two-dimensional angular correlation of annihilation radiation (2D-ACAR) experiments have been performed on a uniaxially oriented polymer, bisphenol-A polycarbonate. The two-dimensional hole structures of unoriented and oriented polymers, determined from the momentum distributions, are found to be spherical and ellipsoidal, respectively. The average hole radii are determined to be 2.9 Angstrom in the unoriented sample and between 2.3 and 3.8 Angstrom in the oriented sample. Applications of the 2D-ACAR method to image the three-dimensional hole structures of polymeric materials are discussed.