In this paper, a CDMA-based medium access control (MAC) scheme in underwater acoustic sensor networks is proposed, in which a periodic sleeping mode is jointly employed for the purpose of saving energy. A hierarchical tree-topology is considered where a staggered wakeup schedule is used across the multiple hierarchical levels from bottom-nodes to a top-node to allow long propagation delay of the underwater acoustic channel. The sensor nodes located in the same hierarchical level are multiplexed by means of different orthogonal codes. Both single-code and multi-code allocation schemes are analyzed. Finally, the proposed scheme is compared with Slotted FAMA, which is a representative MAC protocol designed for a multi-hop network, in terms of data throughput.