A newly developed three-dimensional spiral injection scheme for beam insertion into a solenoidal storage ring is reported. A new planned muon g−2/EDM experiment at J-PARC aims to measure g−2 to a factor of 5 better statistical precision and a factor of 100 better sensitivity for the electric dipole moment (EDM) measurement compared to previous experiments. The J-PARC experiment will use a 3-T MRI solenoid magnet as the muon storage ring with a 0.66m diameter to achieve a 1-ppm level of local uniformity. The previous g−2 injection scheme is not applicable for beam injection into a small ring. The new scheme provides a smooth injection utilizing a radial solenoidal fringe field, without causing an error field in the storage volume. The expected storage efficiency is 80% and over, which is to be compared to 3.5% for the previous g−2 experiment. In addition, the ability to control the storage plane is important for the EDM measurement. In this paper, we introduce the conceptual design and required beam parameters in terms of Twiss functions and the expected injection efficiency.