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 singlecode 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.