Quantum state tomography is an important tool in quantum information science for complete characterization of multiqubit states and their correlations. Here we report a method to perform a joint simultaneous readout of two superconducting qubits dispersively coupled to the same mode of a microwave transmission line resonator. The nonlinear dependence of the resonator transmission on the qubit state dependent cavity frequency allows us to extract the full two-qubit correlations without the need for single-shot readout of individual qubits. We employ standard tomographic techniques to reconstruct the density matrix of two-qubit quantum states.