We present an investigation of galaxy-galaxy interactions and their effects on the velocity fields of disc galaxies in combined N-body/hydrodynamic simulations, which include cooling, star formation with feedback, and galactic winds. Rotation curves (RCs) of the gas are extracted from these simulations in a way that follows the procedure applied to observations of distant, small, and faint galaxies as closely as possible. We show that galaxy-galaxy mergers and fly-bys disturb the velocity fields significantly and hence the RCs of the interacting galaxies, leading to asymmetries and distortions in the RCs. Typical features of disturbed kinematics are significantly rising or falling profiles in the direction of the companion galaxy and pronounced bumps in the RCs. In addition, tidal tails can leave strong imprints on the rotation curve. All these features are observable for intermediate redshift galaxies, on which we focus our investigations. We use a quantitative measure for the asymmetry of rotation curves to show that the appearance of these distortions strongly depends on the viewing angle. We also find in this way that the velocity fields settle back into relatively undisturbed equilibrium states after unequal mass mergers and fly-bys. About 1 Gyr after the first encounter, the RCs show no severe distortions anymore. These results are consistent with previous theoretical and observational studies. As an illustration of our results, we compare our simulated velocity fields and direct images with rotation curves from VLT/FORS spectroscopy and ACS images of a cluster at z=0.53 and find remarkable similarities.