As a special type of mobile ad hoc network (MANET), the flying ad hoc network (FANET) has the potential to enable a variety of emerging applications in both civilian wireless communications (e.g., 5G and 6G) and the defense industry. The routing protocol plays a pivotal role in FANET. However, when designing the routing protocol for FANET, it is conventionally assumed that the aerial nodes move randomly. This is clearly inappropriate for a mission-oriented FANET (MO-FANET), in which the aerial nodes typically move toward a given destination from given departure point(s), possibly along a roughly deterministic flight path while maintaining a well-established formation, in order to carry out certain missions. In this paper, a novel cyber-physical routing protocol exploiting the particular mobility pattern of an MO-FANET is proposed based on cross-disciplinary integration, which makes full use of the mission-determined trajectory dynamics to construct the time sequence of rejoining and separating, as well as the adjacency matrix for each node, as prior information. Compared with the existing representative routing protocols used in FANETs, our protocol achieves a higher packet-delivery ratio (PDR) at the cost of even lower overhead and lower average end-to-end latency, while maintaining a reasonably moderate and stable network jitter, as demonstrated by extensive ns-3-based simulations assuming realistic configurations in an MO-FANET.