This letter presents a calibration technique for uniform circular array orbital angular momentum systems that can estimate and compensate for gain/phase mismatch among radio-frequency (RF) chains in the transmitter and the receiver simultaneously. The basic idea is that the RF chain mismatch parameters can be estimated from a mathematical model of channel estimates when the ideal channel matrix is known a priori. It is shown that the maximum-likelihood (ML) channel estimation error becomes a zero-mean complex Gaussian random variable, and then, a joint ML solution for the RF mismatch parameters is derived.