We present a 3D Bayesian method to model the kinematics of strongly lensed galaxies from spatially-resolved emission-line observations. This technique enables us to simultaneously recover the lens-mass distribution and the source kinematics directly from the 3D data cube. We have tested this new method with simulated OSIRIS observations for nine star-forming lensed galaxies with different kinematic properties. The simulated rotation curves span a range of shapes which are prototypes of different morphological galaxy types, from dwarf to massive spiral galaxies. We have found that the median relative accuracy on the inferred lens and kinematic parameters are at the level of 1 and 2 per cent, respectively. We have also tested the robustness of the technique against different inclination angles, signal-to-noise ratios, the presence of warps or non-circular motions and we have found that the accuracy stays within a few per cent in most cases. This technique represents a significant step forward with respect to the methods used until now, as the lens parameters and the kinematics of the source are derived from the same 3D data. This enables us to study the possible degeneracies between the two and estimate the uncertainties on all model parameters consistently.
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