This study investigates the feasibility of incorporating coarse reclaimed asphalt pavement (RAP) into steel fiber-reinforced concrete (SFRC) for pavement applications. RAP aggregates obtained from 20-year-old pavements were utilized as a full replacement for natural aggregates in the steel fiber layer. A series of laboratory experiments were conducted to evaluate the mechanical and durability properties of RAP-based SFRC, focusing on flexural strength, compressive strength, splitting tensile strength, water absorption, and sorptivity. The results indicate that while the inclusion of RAP reduces the tensile strength of concrete due to weakened interfacial bonds and increased porosity, the addition of 0.75% by mass steel fibers effectively mitigates these drawbacks by enhancing crack resistance, energy absorption, and stress redistribution. The steel fiber reinforcement significantly improves the flexural and impact resistance of the concrete, making it more suitable for high-traffic pavements and airfield applications where durability and crack resistance are critical. Moreover, despite an increase in water absorption with higher RAP content, sorptivity is reduced due to the asphalt binder coating on RAP aggregates, which limits capillary absorption. This study highlights the potential of optimizing RAP content and fiber reinforcement to develop sustainable and high-performance concrete for road infrastructure.