This paper studies the Raman quantum memory protocol as applied to quantum light with orbital angular momentum. The memory protocol is implemented on an ensemble of three-level cold atoms with the Λ configuration of energy levels. The possibility of storing quantum statistics of light with an orbital momentum is analyzed in the case when the driving field could be treated as a plane wave. The efficiency analysis shows that examined storage and retrieval processes do not cause the efficiency decreasing compared with the spatial multimode memory protocol considered in [T. Golubeva, Y. M. Golubev, O. Mishina, A. Bramati, J. Laurat, and E. Giacobino, Eur. Phys. J. D 66, 275 (2012)EPJDF61434-606010.1140/epjd/e2012-20723-3]. We also present an effective transformation of the orbital angular momentum of a quantum field on a memory cell using the driving field with orbital angular momentum.