Vehicles equipped with Cooperative Adaptive Cruise Control (CACC) have the capability to broadcast their real-time speed and location information via wireless communications. They can also safely operate in multi-vehicle strings while keeping shorter than normal gaps among adjacent vehicles in the high-speed traffic stream. Such capabilities can greatly benefit the management of urban signalized intersections. In this study, we have developed a cooperative signal control algorithm that adopts the CACC datasets and the datasets collected by the traditional fixed traffic sensors to predict the future traffic conditions. The prediction allows the signal controller to assign signal priority to the intersection approach that accommodates the most CACC strings. Such a control strategy can significantly enhance the CACC string operation, which ultimately improves the overall intersection performance. The effectiveness of the algorithm has been tested in a simulated 4-way signalized intersection. The algorithm substantially outperforms the traditional actuated controller as it perceives the traffic flow more comprehensively and assigns the green time resource more efficiently than the traditional controller. Particularly, the average vehicle speed and the average vehicle miles travelled per gallon fuel consumed (MPG) can be increased by more than 10% when the CACC market penetration is 100%. In mixed traffic where CACC fleets frequently interact with manually driven vehicles, the algorithm is found to be more beneficial. The speed and MPG improvement exceed 30% when the CACC market penetration is 40%. The signal control algorithm can bring about significant benefit even when the CACC market penetration is 0%. In this case, it completely relies on the datasets obtained from the traditional traffic sensors. This finding demonstrates the robustness of the algorithm. It makes the proposed algorithm suitable to implement in real-world intersections under various CACC market penetrations and different levels of vehicle connectivity.