We studied the nonlinear parametric interaction of femtosecond fractionally-charged optical vortices in a Raman-active medium. Propagation of such beams was described using the Kirchhoff-Fresnel integrals by embedding a non-integer 2 pi phase step in a Gaussian beam profile. When using fractionally-charged pump or Stokes beams, we observed the production of new topological charge and phase discontinuities in the Raman field. These newly generated fractionally-charged Raman vortex beams were found to follow the same orbital angular momentum algebra derived by Strohaber et al (2012 Opt. Lett. 37 3411) for integer vortex beams.