This paper studies the joint optimization of precoding, transmit power and data rate allocation for energy-efficient full-duplex (FD) cloud radio access networks (C-RANs). A new nonconvex problem is formulated, where the ratio of total sum rate to total power consumption is maximized, subject to the maximum transmit powers of remote radio heads and uplink users. An iterative algorithm based on successive convex programming is proposed with guaranteed convergence to the Karush-Kuhn-Tucker solutions of the formulated problem. Numerical examples confirm the effectiveness of the proposed algorithm and show that the FD C-RANs can achieve a large gain over half-duplex C-RANs in terms of energy efficiency at low self-interference power levels.