This paper presents Reward Based Routing Protocol (RBRP), a novel routing protocol for wireless mesh networks, that aims at reducing and fairly distributing the Electromagnetic Field (EMF) Exposure caused by wireless transmissions. The basis of this protocol is a reward-based scheme in which intermediate nodes forward packets and receive a reward proportional to the degree of exposure they generate. By means of a simulation campaign over the NS-3 framework, we assess that RBRP clearly outperforms a legacy approach in terms of exposure, while it does not show a worse behaviour, when considering other figures of merit.