Cadmium arsenide (Cd3As2) is known for its inverted band structure and ultra-high electron mobility. It has been theoretically predicted and also confirmed by ARPES experiments to exhibit a 3D Dirac semimetal phase containing degenerate Weyl nodes. From magneto-transport measurements in high quality single crystals of Cd3As2, a small effective mass m(*) ≈ 0.05 me is determined from the Shubnikov-de Haas (SdH) oscillations. In certain field orientations, we find a splitting of the SdH oscillation frequency in the FFT spectrum suggesting a possible lifting of the double degeneracy in accord with the helical spin texture at outer and inner Fermi surfaces with opposite chirality predicted by our ab initio calculations. Strikingly, a large antisymmetric magnetoresistance with respect to the applied magnetic fields is uncovered over a wide temperature range in needle crystal of Cd3As2 with its long axis along [112] crystal direction. It reveals a possible contribution of intrinsic anomalous velocity term in the transport equation resulting from a unique 3D Rashba-like spin splitted bands that can be obtained from band calculations with the inclusion of Cd antisite defects.