In the past few years, energy conservation has been the main focus of researchers working on wireless sensor networks. One of the main technique to save energy is to deactivate periodically the radio module of sensor nodes: nodes alternate periods of activity and periods of inactivity, which is referred to as their duty-cycle. In this paper, we focus on asynchronous duty-cycle mechanisms, as these mechanisms are usually simple, do not require time synchronization and support network changes. We propose an asynchronous MAC protocol based on blind rendezvous and random wake-up. Our protocol is based on a modification of the IEEE 802.15.4 standard, where activities start at a random time within each activity cycle. Our simulations show that our protocol can achieve a good performance under various scenarios, for small duty cycles (ranging from 0.1% to 5%).