In this work, we designed and simulated a novel air-core As2S3 ring fiber that supports orbital angular momentum (OAM) modes. By optimizing the structure parameters of the designed fiber to effectively tailor its chromatic dispersion, a near-zero flat dispersion profile with a total of <; ±30 ps/nm/km variation over 3380-nm bandwidth from 2025 nm to 5405 nm is achieved for OAM1,1 mode. After launching a 100-fs 70-kW hyperbolic secant pulse into an 8-mm air-core As2S3 ring fiber, a light-carrying OAM supercontinuum is numerically formed beyond two-octave range, covering 5717nm bandwidth from 1182 nm to 6897 nm at -30dB. Furthermore, the generated supercontinuum is highly coherent across the whole spectral range. This can serve as an effective manner to expand the spectral coverage of the OAM beams for various applications.