In this paper, we study the issue of routing in a vehicular ad hoc network with the assistance of sparsely deployed auxiliary relay nodes at some road intersections in a city. In such a network, vehicles keep moving, and relay nodes are static. The purpose of introducing auxiliary relay nodes is to reduce the end-to-end packet delivery delay. We propose a sparsely deployed relay node assisted routing (SRR) algorithm, which differs from existing routing protocols on how routing decisions are made at road intersections where static relay nodes are available such that relay nodes can temporarily buffer a data packet if the packet is expected to meet a vehicle leading to a better route with high probability in certain time than the current vehicles. We further calculate the joint probability for such a case to happen on the basis of the local vehicle traffic distribution and also the turning probability at an intersection. The detailed procedure of the protocol is presented. The SRR protocol is easy to implement and requires little extra routing information. Simulation results show that SRR can achieve high performance in terms of end-to-end packet delivery latency and delivery ratio when compared with existing protocols.