This paper establishes a distributed distributionally robust optimization model of the AC/DC distribution network driven by historical data. Firstly, this paper analyzes the historical data and uses Copula theory to establish the joint probability distribution of wind power error and forecast power, then obtains the conditional probability distribution of error under certain forecast power. Secondly, this paper decouples the AC/DC hybrid distribution network into AC subnetwork and DC subnetwork, and takes the minimum comprehensive operating cost of each as the optimization goal, among which the carbon trading mechanism is introduced in the AC subnet optimization, and the distributed optimization model of AC-DC distribution network is established. Thirdly, in view of the uncertainty of wind power, an ambiguous set based on KL divergence is constructed. This paper takes the aforementioned error probability distribution as a reference distribution, and the proposed model is converted into a single-layer linear optimization target by using Lagrange dualism theory, and then the distributed solution is performed by using the alternating direction multiplier method. Simulation experiments are carried out on the modified 33-nodes AC/DC distribution network system model, and the results show that the proposed model can effectively reduce the carbon emissions on the distribution network side and significantly improve the consumption capacity of wind power.