Orbital angular momentum (OAM) multiplexing technology is expected as one of the prospective candidates for sustaining the further increment of data-transmission capacity in the optical communication systems. Advanced multiplexing technology of combining OAM-based mode division multiplexing (MDM) in the multicore fiber (MCF) with wavelength division multiplexing (WDM) can further improve the transmission rate and spectrum efficiency in the communication systems. In this paper, a multi-ring-air-core fiber (MRACF) supporting thousands of OAM modes is designed and analyzed. The tradeoffs between ring number/density and their corresponding system performance parameters in this fiber are systematically investigated. Based on the analytical results, MRACF with 37 rings can support a record high 4440 radially fundamental OAM modes at 1550 nm, featuring <−53 dB inter-ring crosstalk and >5.67 × 10−4 intra-ring modal effective refractive index difference. Furthermore, a record-high 4144 radially fundamental OAM modes with <−40 dB inter-ring crosstalk can be supported across C and L bands from 1530 nm to 1625 nm, which is one order of magnitude larger than the number of linearly polarized (LP) modes or supermodes ever reported within one single fiber.