In this paper, we consider channel access in Unamnanned Aerial Vehicles (UAVs) networks where a ground station is equipped with Successive Interference Cancellation (SIC) capability. The problem at hand is to derive a transmission schedule for UAVs to communicate with a ground station frequently, and with minimal collisions. We first formulate a stochastic optimization problem before introducing a novel distributed Learning Medium Access Control (MAC), aka L-MAC, protocol. A key novelty of L-MAC is that it allows UAVs to learn the best orientation that results in the highest decoding success. Our simulation results show that L-MAC achieves a throughput that is 68% higher than the well-known Aloha protocol without SIC and 28% than Aloha with SIC.