We propose a cooperative MAC protocol with rapid relay selection (RRS-CMAC) to improve the cooperation efficiency and multiple access performance in wireless ad hoc networks. In this protocol, if the data rate between a sender and its recipient is low, an optimal relay is selected by a rate differentiation phase (RDP), priority differentiation phase (PDP), and contention resolution phase (CRP) for relays with the same priority. In the RDP, each contending relay determines its data rate level based on the data rate from the sender to itself and that from itself to the recipient, and then broadcasts busy tones to its neighbor nodes or senses the channel according to the values of its binary digits, which are determined by its data rate level. Relays with the highest data rate levels win and continue to the next phase. In PDP, these winning relays send busy tones or sense the channel according to their own priority values, with the highest priority relays winning in this phase. Then CRP is performed using k-round contention resolution (k-CR) to select a unique optimal relay. Relays sending busy tones earliest and for the longest duration proceed to the next round, while others, sensing a busy tone, subsequently withdraw from contention. A packet piggyback mechanism is adopted to allow data packet transmission without reservation if the winning relay has a packet to send, and the direct transmission rate to its recipient is high. This reduces reservation overhead and improves channel utilization. Both theoretical analysis and simulation results show that the throughput of the proposed protocol is better than those of the CoopMACA and 2rcMAC protocols.