Cloud radio access networks (C-RAN) enable a network platform for beyond the fifth generation of communication networks (B5G), which incorporates the advances in cloud computing technologies to modern radio access networks. Recently, rate splitting multiple access (RSMA), relying on multi-antenna rate splitting (RS) at the transmitter and successive interference cancellation (SIC) at the receivers, has been shown to manage the interference in multi-antenna communication networks efficiently. This paper considers applying RSMA in C-RAN. We address the practical challenge of a transmitter that only knows the statistical channel state information (CSI) of the users. To this end, the paper investigates the problem of stochastic coordinated beamforming (SCB) optimization to maximize the ergodic sum-rate (ESR) in the network. Furthermore, we propose a scalable and robust RS scheme where the number of the common streams to be decoded at each user scales linearly with the number of users, and the common stream selection only depends on the statistical CSI. The setup leads to a challenging stochastic and non-convex optimization problem. A sample average approximation (SAA) and weighted minimum mean square error (WMMSE) based algorithm is adopted to tackle the intractable stochastic non-convex optimization and guarantee convergence to a stationary point asymptotically. The numerical simulations demonstrate the efficiency of the proposed RS strategy and show a gain up to 27% in the achievable ESR compared with state-of-the-art schemes, namely treating interference as noise (TIN) and non-orthogonal multiple access (NOMA) schemes.