Security enhancement is important in terms of both classical and quantum information. The recent development of a quantum storage device is noteworthy, and a coherence time of one second or longer has been demonstrated. On the other hand, although the encryption of a quantum bit or quantum memory has been proposed theoretically, no experiment has yet been carried out. Here we report the demonstration of a quantum memory with an encryption function that is realized by scrambling and retrieving the recorded quantum phase. We developed two independent Ramsey interferometers on an atomic ensemble trapped below a persistent supercurrent atom chip. By operating the two interferometers with random phases, the quantum phase recorded by a pulse of the first interferometer was modulated by the second interferometer pulse. The scrambled quantum phase was restored by employing another pulse of the second interferometer with a specific time delay. This technique paves way for improving the security of quantum information technology.