This work studies distributed compression for the uplink of a cloud radio access network, where multiple multi-antenna base stations (BSs) communicate with a central unit, also referred to as cloud decoder, via capacity-constrained back-haul links. Distributed source coding strategies are potentially beneficial since the signals received at different BSs are correlated. However, they require each BS to have information about the joint statistics of the received signals across the BSs, and are generally sensitive to uncertainties regarding such information. Motivated by this observation, a robust compression method is proposed to cope with uncertainties on the correlation of the received signals. The problem is formulated using a deterministic worst-case approach, and an algorithm is proposed that achieves a stationary point for the problem. From numerical results, it is observed that the proposed robust compression scheme compensates for a large fraction of the performance loss induced by the imperfect statistical information.