We propose a new hybrid software-defined networking (SDN) approach, Cloud-Assisted Routing (CAR), that utilizes high computation and memory power of cloud services by splitting both control and data plane functions between a local router and a remote cloud computing platform. Instead of a complete separation of the two planes, our approach maintains most of the control plane at the cloud and the least of it at the local router, and vice versa for the data plane. We present the architectural view of CAR and results from an initial prototype of forwarding table size reduction using CAR. We discuss possible intra- and inter-domain optimizations by highlighting the use-cases of multi-cloud design paradigm and perform a cost comparison between legacy router vs. CAR to identify the break-even points and key components that make CAR monetarily beneficial.