We study the properties of kinematically disturbed galaxies in the SAMI Galaxy Survey using a quantitative criterion, based on kinemetry (Krajnovic et al.). The approach, similar to the application of kinemetry by Shapiro et al. uses ionised gas kinematics, probed by H{alpha} emission. By this method 23+/-7% of our 360-galaxy sub-sample of the SAMI Galaxy Survey are kinematically asymmetric. Visual classifications agree with our kinemetric results for 90% of asymmetric and 95% of normal galaxies. We find stellar mass and kinematic asymmetry are inversely correlated and that kinematic asymmetry is both more frequent and stronger in low-mass galaxies. This builds on previous studies that found high fractions of kinematic asymmetry in low mass galaxies using a variety of different methods. Concentration of star forma- tion and kinematic disturbance are found to be correlated, confirming results found in previous work. This effect is stronger for high mass galaxies (log(M*) > 10) and indicates that kinematic disturbance is linked to centrally concentrated star formation. Comparison of the inner (within 0.5Re) and outer H{alpha} equivalent widths of asymmetric and normal galaxies shows a small but significant increase in inner equivalent width for asymmetric galaxies.