Neighbor discovery is a fundamental requirement and need be done frequently in underwater acoustic networks (UANs) with floating node mobility. In hostile environments, neighbor discovery is vulnerable to the wormhole attack by which the adversary uses secret wormhole links to make distant nodes falsely accept each other as a neighbor. The wormhole attack may lead to many undesirable consequences and cannot be solved by cryptographic methods. Existing wormhole defenses for ground wireless networks cannot be directly applied to UANs where most of their assumptions no longer hold. This paper presents a suite of novel protocols to enable wormhole-resilient secure neighbor discovery in UANs. Our protocols are based on the Direction of Arrival (DoA) estimation of acoustic signals, a basic functionality readily available in current UANs. The proposed protocols can thwart the wormhole attack with overwhelming probability without conventional hard requirements on secure and accurate time synchronization and localization. Detailed theoretical analysis and simulation results confirm the high performance of the proposed protocols.