Conventional Call Admission Control (CAC) schemes are based on stand-alone Radio Access Networks (RAN) Base Station (BS) architectures which have their independent and fixed spectral and computing resources, which are not shared with other BSs to address their varied traffic needs, causing poor resource utilization, and high call blocking and dropping probabilities. It is envisaged that in future communication systems like 5G, Cloud RAN (C-RAN) will be adopted in order to share this spectrum and computing resources between BSs in order to further improve the Quality of Service (QoS) and network utilization. In this paper, an intelligent Elastic CAC scheme using Fuzzy Logic in C-RAN is proposed. In the proposed scheme, the BS resources are consolidated to the cloud using virtualization technology and dynamically provisioned using the elasticity concept of cloud computing in accordance to traffic demands. Simulations shows that the proposed CAC algorithm has high call acceptance rate compared to conventional CAC.