In this work, we present a numerical design of an air-core vortex polymer optical fiber in CYTOP that propagates modes with orbital angular momentum (OAM) at a visible wavelength of 633 nm. In this fiber, we show a stable propagation of up to 14 OAM states, even under perturbations such as changes in the circularity that leads to elliptic rings in the fabrication processes. Considering ellipticity less than 2%, we obtain charge weights lower than-38 dB between neighbor OAM modes, and around-0.25 dB for OAM modes of the same value, showing that OAM modes are uncoupled after perturbation like the ellipticity.