To determine the importance of merging galaxies to galaxy evolution, it is necessary to design classification tools that can identify the different types and stages of merging galaxies. Previously, using GADGET-3/SUNRISE simulations of merging galaxies and linear discriminant analysis (LDA), we created an accurate merging galaxy classifier based on imaging predictors. Here, we develop a complementary tool, based on stellar kinematic predictors, derived from the same simulation suite. We design mock stellar velocity and velocity dispersion maps to mimic the specifications of the Mapping Nearby Galaxies at Apache Point (MaNGA) integral field spectroscopy (IFS) survey, and utilize an LDA to create a classification, based on a linear combination of 11 kinematic predictors. The classification varies significantly with mass ratio; the major (minor) merger classifications have a mean statistical accuracy of 80% (70%), a precision of 90% (85%), and a recall of 75% (60%). The major mergers are best identified by predictors that trace global kinematic features, while the minor mergers rely on local features that trace a secondary stellar component. While the kinematic classification is less accurate than the imaging classification, the kinematic predictors are better at identifying post-coalescence mergers. A combined imaging + kinematic classification has the potential to reveal more complete merger samples from imaging and IFS surveys such as MaNGA. We note that since the suite of simulations used to train the classifier covers a limited range of galaxy properties (i.e., the galaxies are of intermediate mass, and disk-dominated), the results may not be applicable to all MaNGA galaxies.