This paper proposes a multipath routing protocol called cross-layer multipath AODV (CM-AODV) for wireless ad hoc networks, which selects multiple routes on demand based on the signal-to-interference plus noise ratio (SINR) measured at the physical layer. Note that AODV (Ad hoc On-demand Distance Vector) is one of the most popular routing protocols for mobile ad hoc networks. Each time a route request (RREQ) message is forwarded hop by hop, each forwarding node updates the route quality which is defined as the minimum SINR of serialized links in a route and is contained in the RREQ header. While achieving robust packet delivery, the proposed CM-AODV is amenable to immediate implementation using existing technology by neither defining additional packet types nor increasing packet length. Compared to the conventional multipath version of AODV (which is called AOMDV), CM-AODV assigns the construction of multiple paths to the destination node and makes it algorithmically simple, resulting in the improved performance of packet delivery and the less overhead incurred at intermediate nodes. Our performance study shows that CM-AODV significantly outperforms AOMDV in terms of packet delivery ratio and average end-to-end delay, and results in less routing overhead.