Ad hoc network is a collection of wireless mobile nodes that dynamically form a temporary network without the use of any existing network infrastructure or centralized administration. A cognitive radio is a radio that can change its transmitter parameters based on interaction with the environment in which it operates. The basic idea of cognitive radio networks is that the unlicensed devices (cognitive radio users or secondary users) need to vacate the spectrum band once the licensed device (primary user) is detected. Cognitive capability and re-configurability are the key characteristics of cognitive radio. Routing is an important issue in Mobile Cognitive Radio Ad Hoc Networks (MCRAHNs). In this paper, a survey of routing protocols for mobile cognitive radio ad networks is discussed.