Photonic quasicrystals are unique structures having long-range order but no periodicity. It has been found that quasiperiodic structures give rise to unusual phenomena and properties that have not been observed in periodic structures. Recently, it has been reported that introducing quasi-periodic structures of microscopic air holes in optical fibers can give rise to a unique dispersion property such as almost zero ultra-flattened chromatic dispersion and large mode area dispersion compensating fiber. In this paper, we introduce a ring core photonic quasicrystal fiber (PQF) and its optical properties are theoretically analyzed. The chromatic dispersion properties of doped ring core PQF, are investigated along with their dependence on the proposed defect parameters using 3D full-vectorial Beam Propagation Method (BPM) and plane wave expansion method.