Unmanned aerial vehicles (UAVs) are deployed in various mission-critical applications to collect sensitive data and disseminate it to the server placed on the ground station. Users mostly require real-time data from the drones, instead of the information stored by the server, in specific applications to perform timely actions. However, performing real-time communication with a drone through the public communication channel, which exposed to different security risks mandates an authenticated key exchange between users and drones in the Internet of Drones (IoD) networks for enabling users to communicate securely with the drone through the public communication infrastructure. This paper proffers a resource-efficient authentication scheme for the IoD networks, called REAS-IoD. The proposed REAS-IoD utilizes the lightweight hash function and authenticated encryption primitive, known as ACE to accomplish the AKE process securely. In REAS-IoD, a user's authentication is performed, followed by establishing a secure session key (SK) between a specific drone and the user, for future encrypted communication. The SK's security is established utilizing a random oracle model. A comparative study demonstrates that REAS-IoD requires fewer resource, without compromising security and privacy features than related eminent security schemes.