This letter presents a wideband blind calibration method for uniform circular array (UCA) orbital angular momentum (OAM) systems without the prior knowledge of the positions and attitudes of the transmit and receive UCAs. The basic idea is to rewrite the maximum-likelihood estimation (MLE) for all parameters as an optimization problem over a Lie group which can represent the positions and attitudes of the UCAs. Then an accelerated Levenberg-Marquardt algorithm is implemented to solve this optimization problem by utilizing the sparsity in the iteration process. Simulation results show that the proposed wideband blind calibration method can estimate the gain/phase errors and the positions and attitudes of the transmit and receive UCAs simultaneously and improve the achievable spectral efficiency of the UCA OAM communication system efficiently.