In I/Q receivers characterized by direct conversion or low-IF operations, phase imbalance between the I and Q branches stands for a substantial issue which may degrade significantly the overall link performance. An alternative solution to high cost analog components with small tolerances which make the I/Q imbalance effect negligible is to estimate and compensate it digitally. In this paper we present a novel data aided (DA) joint estimator of the carrier phase offset and the I/Q phase imbalance derived following the maximum likelihood (ML) criterion. The performance accuracy analysis proves that the proposed estimator is efficient and achieves its vector Cramer-Rao lower bound (VCRLB). Simulation results in terms of BER performance of uncoded and turbo coded systems show that the proposed imbalance compensation method, at the cost of a low additional implementation complexity of the digital receiver, allows negligible performance degradation in the context of multi-level modulation formats, such as 16-QAM and 64-QAM.