Underwater Acoustic Sensor Networks (UASN) have two important limitations: a very aggressive (marine) environment, and the use of acoustic signals. This means that the techniques for terrestrial wireless sensor networks (WSN) are not applicable. This paper proposes a routing protocol called “Self-Organizing and Scalable Routing Protocol” (SOSRP) which is decentralized and based on tables residing in each node. A combination of the hop value to the collector node and the distance is used as a criterion to create routes leading to the sink node. The expected functions of the protocol include self-organization of the routes, tolerance to failures and detection of isolated nodes. Through the implementation of SOSRP in Matlab and a model of propagation and energy being appropriate for marine environment, performance results are obtained in different scenarios (varying both nodes and transmission range) that include parameters such as end-to-end packet delay, consumption of energy or length of the created routes (with and without failure). The results obtained show a stable, reliable and suitable operation for the deployment and operation of nodes in UASN networks.