This research introduces a numerical design of an air-core vortex polymer optical fiber in cyclic transparent optical polymer (CYTOP) that propagates 32 orbital angular momentum (OAM) modes, i.e., it may support up to 64 stable OAM-states considering left- and right-handed circular polarizations. This fiber seeks to be an alternative to increase the capacity of short-range optical communication systems multiplexed by modes, in agreement with the high demand of low-cost, insensitive-to-bending and easy-to-handle fibers similar to others optical fibers fabricated in polymers. This novel fiber possesses unique characteristics: a diameter of 50 µm that would allow a high mechanical compatibility with commercially available polymer optical fibers, a difference of effective index between neighbor OAM modes of around 10−4 over a bandwidth from 1 to 1.6 µm, propagation losses of approximately 15 × 10−3 dB/m for all OAM modes, and a very low dispersion for OAM higher order modes (±l = 16) of up to +2.5 ps/km-nm compared with OAM lower order modes at a telecom wavelength of 1.3 µm, in which the CYTOP exhibits a minimal attenuation. The spectra of mutual coupling coefficients between modes are computed considering small bends of up to 3 cm of radius and slight ellipticity in the ring of up to 5%. Results show lower-charge weights for higher order OAM modes.