Cloud Radio Access Network is foreseen as one of the key features of the future 5G mobile communication standard. In this context, all the baseband processing is intended to be performed on CPUs in order to keep a high level of flexibility. The challenge is then to propose efficient software implementations of baseband processing algorithms that guarantee a sufficient throughput, while limiting the energy consumption. In this paper, as an alternative to general purpose processors, we propose an implementation of an Application Specific Instruction set Processor customized for the Successive Cancellation decoding of polar codes. The resulting software decoder achieves throughputs similar to state-of-the-art ARM processor implementations, while reducing the energy consumption by a factor 10.