Acousto-optic interaction in optical fiber is examined from the perspective of copropagating optical and acoustic vortex modes. Calculation of the acousto-optic coupling coefficient between different optical modes leads to independent conservation of spin and orbital angular momentum of the interacting photons and phonons. We show that the orbital angular momentum of the acoustic vortex can be transferred to a circularly polarized fundamental optical mode to form a stable optical vortex in the fiber carrying orbital angular momentum. The technique provides a useful way of generating stable optical vortices in the fiber medium.