Vehicular communications (VCs) protocols offer useful contributions in the context of accident prevention thanks to the transmission of alert messages. This is even truer at road intersections since these areas exhibit higher collision risks and accidents rate. On the other hand, non-orthogonal multiple access (NOMA) has been show to be a suitable candidate for five generation (5G) of wireless systems. In this paper, we propose and evaluate the performance of VCs protocol at road intersections, named adaptive cooperative NOMA (ACN) protocol. The transmission occurs between a source and two destinations. The transmission is subject to interference originated from vehicles located on the roads. The positions of the interfering vehicles follow a Poison point process (PPP). First, we calculate the outage probability related to ACN protocol, and closed form expressions are obtained. Then we compare it with other existing protocols in the literature. We show that ACN protocol offers a significant improvement over the existing protocols in terms of outage probability, especially at the intersection. We show that the performance of ACN protocol increases compared to other existing protocols for high data rates. The theoretical results are verified with Monte-Carlo simulations.