We report on the generation of an off-axis vortex with tunable non-integer orbital angular momentum (OAM), generated using an idler-resonant mid-infrared optical parametric oscillator (OPO) based on KTiOAsO4. The design of the OPO enables the OAM of the signal and idler outputs to be varied from 0 to 1 through precise adjustment of cavity length. The maximum vortex output energies at 1.5 and 3.5 μm were 1.95 and 1.1 mJ, respectively, and were obtained at a maximum pump energy of 20 mJ. The means by which the OAM was shared between the signal and idler fields was theoretically examined by modeling the spatial coupling among the pump, signal, and idler fields within the cavity. This work offers a unique means by which exotic vortex laser beams with tunable non-integer OAM can be generated and tuned simply through cavity length adjustments.