Internet of Underwater Things (IoUT) systems comprising tens or hundreds of underwater acoustic communication nodes will become feasible in the near future. The development of scalable networking protocols is a key enabling technology for such IoUT systems, but this task is challenging due to the fundamental limitations of the underwater acoustic communication channel: extremely slow propagation and limited bandwidth. The aim of this paper is to propose the JOIN protocol to enable the integration of new nodes into an existing IoUT network without the control overhead of typical state-of-the-art solutions. The proposed solution is based on the capability of a joining node to incorporate local topology and schedule information into a probabilistic model that allows it to choose when to join the network to minimize the expected number of collisions. The proposed approach is tested in numerical simulations and validated in two sea trials. The simulations show that the JOIN protocol achieves fast convergence to a collision-free solution, fast network adaptation to new nodes, and negligible network disruption due to collisions caused by a joining node. The sea trials demonstrate the practical feasibility of this protocol in real UAN deployments and provide valuable insight for future work on the trade-off between control overhead and reliability of the JOIN protocol in a harsh acoustic communication environment.