Voice over IP (VoIP) requires a Call Admission Control (CAC) mechanism in WiFi networks to preserve VoIP packet flows from excessive network delay or packet loss. Ideally, this mechanism should be integrated with the operational scenario, guarantee the quality of service of active calls, and maximize the number of concurrent calls. This paper presents a novel CAC scheme for VoIP in the context of a WiFi access network deployed with Unmanned Aerial Vehicles (UAVs) that relay to a backhaul 5G network. Our system, named Codec-Optimization CAC (CO-CAC), is integrated into each drone. It intercepts VoIP call control messages and decides on the admission of every new call based on a prediction of the WiFi network’s congestion level and the minimum quality of service desired for VoIP calls. To maximize the number of concurrent calls, CO-CAC proactively optimizes the codec settings of active calls by exchanging signaling with VoIP users. We have simulated CO-CAC in a 50 m 50 m scenario with four UAVs providing VoIP service to up to 200 ground users with IEEE 802.11ac WiFi terminals. Our results show that without CAC, the number of calls that did not meet a minimum quality level during the simulation was 10% and 90%, for 50 and 200 users, respectively. However, when CO-CAC was in place, all calls achieved minimum quality for up to 90 users without rejecting any call. For 200 users, only 25% of call attempts were rejected by the admission control scheme. These results were narrowly worse when the ground users moved randomly in the scenario.