We report on a high-power, continuous-wave source of optical vortices tunable in the mid-infrared (mid-IR) wavelength range. Using the orbital angular momentum (OAM) conservation of the parametric processes and the threshold conditions of the cavity modes of the singly resonant optical parametric oscillator (SRO), we have transferred the OAM of the pump beam at the near-infrared wavelength to the idler beam tunable in the mid-IR. Pumped with a vortex beam of order lp=1 at 1064 nm, the SRO, configured in a four curved mirror-based ring cavity with a 50 mm long MgO-doped periodically poled LiNbO3 crystal, produces an idler beam with an output power in excess of 2 W in a vortex spatial profile with the order li=1, tunable across 2217-3574 nm and corresponding signal beam in Gaussian intensity distribution across 1515-2046 nm. For pump vortices of the order lp=1 and 2, and a power of 22 W, the SRO produces idler vortices of the same order as that of the pump beam with a maximum power of 5.23 and 2.3 W, corresponding to near-IR to mid-IR vortex conversion efficiency of 23.8% and 10.4%, respectively. The idler vortex beam has a spectral width, and a passive rms power stability of 101 MHz and 4.9% over 2 h, respectively.