The complex interactions between orbital angular momentum (OAM) light and atoms are particularly intriguing in the areas of quantum optics and quantum information science. Building a versatile high-dimensional quantum network needs broad spiral-bandwidth for preparing higher-quanta OAM mode and resolving the bandwidth mismatch in spatial space and etc. Here, we experimentally demonstrate a broad spiral-bandwidth quantum interface between photon and memory. Through twisted fields of the writing and reading, the correlated OAM distribution between photon and memory is significantly broadened. This broad spiral-bandwidth quantum interface could be spanned in multiplexing regime and could work in high-quanta scenario with capability of |l|=30, and we demonstrate the entanglement within 2-D subspace with a fidelity of 80.5text{textpm}4.8% for high l. Such state-of-the-art technology to freely control the spatial distribution of OAM memory is very helpful to construct high-dimensional quantum networks and provides a benchmark in the field of actively developing methods to engineer OAM single photon from matters.