We present spatially resolved stellar and/or ionized gas kinematic properties for a sample of 103 interacting galaxies, tracing all merger stages: close companions, pairs with morphological signatures of interaction, and coalesced merger remnants. We compare our sample with 80 non-interacting galaxies. We measure for the stellar and the ionized gas components the major (projected) kinematic position angles (PA$_{\mathrm{kin}}$, approaching and receding) directly from the velocity fields with no assumptions on the internal motions. This method allow us to derive the deviations of the kinematic PAs from a straight line ($δ$PA$_{\mathrm{kin}}$). Around half of the interacting objects show morpho-kinematic PA misalignments that cannot be found in the control sample. Those misalignments are present mostly in galaxies with morphological signatures of interaction. Alignment between the kinematic sides for both samples is similar, with most of the galaxies displaying small misalignments. Radial deviations of the kinematic PA from a straight line in the stellar component measured by $δ$PA$_{\mathrm{kin}}$ are large for both samples. However, for a large fraction of interacting galaxies the ionized gas $δ$PA$_{\mathrm{kin}}$ is larger than typical values derived from isolated galaxies (48%), making this parameter a good indicator to trace the impact of interaction and mergers in the internal motions of galaxies. By comparing the stellar and ionized gas kinematic PA, we find that 42% (28/66) of the interacting galaxies have misalignments larger than 16 degrees, compared to 10% from the control sample. Our results show the impact of interactions in the internal structure of galaxies as well as the wide variety of their velocity distributions. This study also provides a local Universe benchmark for kinematic studies in merging galaxies at high redshift. ; Comment: 24 pages,11 Figures, Accepted for publication in Astronomy & Astrophysics. The entire set of stellar and ionized gas velocity fields of the interacting/merging sample will be available in the electronic version of the journal