Unmanned aerial vehicles (UAV), an emerging architecture that embodies flying ad-hoc networks, face critical privacy and security challenges, mainly when engaged in data-sensitive missions. Therefore, message authentication is a crucial security feature in drone communications. This paper presents a Blockchain-based Efficient, and Trusted Authentication scheme for UAV communication, BETA-UAV, which exploits the inherent properties of blockchain technology concerning memorability and is immutable to record communication sessions via transactions using a smart contract. The smart contract in BETA-UAV allows participants to publish and call transactions from the blockchain network. Furthermore, transaction addresses are proof of freshness and trustworthiness for subsequent transmissions. Furthermore, we investigated their ability to resist active attacks, such as impersonation, replaying, and modification. In addition, we evaluate the gas costs associated with the functions of the smart contract by implementing a BETA-UAV on the Ethereum public blockchain. A comparison of the computation and communication overheads shows that the proposed approach can save significant costs over traditional techniques.