The non-volatile metal-oxide resistive random access memory (ReRAM) is an emerging alternative for the current memory technologies. The unique capability of ReRAM to perform analog and digital arithmetic and logic operations has enabled this technology to incorporate both computation and memory capabilities on the same unit. Due to this interesting property, there is a growing trend in recent years to implement emerging data-intensive applications on ReRAM structures. A typical ReRAM-based processing-in-memory architecture may consist tens to hundreds of ReRAM units (mats) that can either store or process data. To support such large-scale ReRAM structure, this paper proposes a scalable network-on-ReRAM architecture. The proposed network employs a novel associative router architecture, designed based on the ReRAM-based content-addressable memories. With the in-memory packet processing capability, this router yields higher throughput and resource utilization levels than a conventional router. This router is technology compatible with ReRAM and as our evaluations show, employing it to build a network-on-ReRAM makes the emerging ReRAM-based processing-in-memory architectures more scalable and performance-efficient.