Raman scattering among conventional linearly polarized (LP) modes in single mode optical fibers is generally accepted as a promising way to achieve distributed amplification due to the fact that Raman amplification may provide gain at any wavelength, determined by the used pump wavelength, and excellent noise performance. Here, we show that Raman scattering among orbital angular momentum (OAM) modes in optical fibers have similar properties. We show theoretically that the Raman gain among OAM modes is independent on the topological charge of the OAM modes and that the gain efficiency when the pump and signal are parallel (orthogonally) polarized is similar to the Raman scattering among LP modes in parallel (orthogonal) states of polarization. In addition, we experimentally characterize Raman gain among OAM modes in a fiber supporting multiple OAM modes for both the pump and signal. Finally, we discuss the impact of polarization mode dispersion.