The Energy Harvesting-aware Distributed Queuing access protocol (EH-DQ) is presented in this paper as a novel Medium Access Control protocol for wireless Machineto-Machine networks with energy harvesting capabilities. EHDQ is theoretically modeled to analyze its performance. A performance comparison with a Time Division Multiple Access (TDMA) and an EH-aware Reservation Dynamic Frame SlottedALOHA (EH-RDFSA) shows its superior performance. While TDMA requires updated network information to maintain a collision-free schedule and EH-RDFSA requires to estimate the number of contenders per frame to dynamically adjust the frame length, EH-DQ uses short and fixed frame lengths and does not require knowledge of the network topology or the number of end-devices in advance.