The spatial modes of light, carrying a quantized amount of orbital angular momentum (OAM), is one of the excellent candidates that provides access to high-dimensional quantum states, which essentially makes it promising towards building high-dimensional quantum networks. In this paper, we report the storage and retrieval of photonic qubits encoded with OAM state in the cold atomic ensemble, achieving an average conditional fidelity above 98% and retrieval efficiency around 65%. The photonic OAM qubits are encoded with weak coherent states at the single-photon level and the memory is based on electromagnetically induced transparency in an elongated cold rubidium atomic ensemble. Our work constitutes an efficient node that is needed towards high dimensional and large scale quantum networks.