Inertial particle separation using passive hydrodynamic forces has attracted great attention in the microfluidics community because of its operation simplicity and high throughput sample processing. Due to the passive nature of inertial microfluidics, each inertial sorting device is typically fixed to a certain cut-off size for particle separation that is mainly dependent on the channel geometry and dimensions, which however lacks tunability in the separation threshold to fulfill the needs of different sorting applications. In this work, we explore the use of non-Newtonian viscoelastic fluids to achieve size-tunable elasto-inertial particle focusing and sorting in a microfluidic device with reverse wavy channel structures. The balance and competition among inertial lift force, Dean drag force and the controllable elastic lift force give rise to interesting size-based particle focusing phenomena with tunability in the equilibrium focusing positions. Seven differently sized fluorescent microspheres (0.3, 2, 3, 5, 7, 10 and 15 μm) are used to investigate the effects of the flow rate, viscoelastic fluid concentration and particle size on the tunable elasto-inertial focusing behavior. With the sorting tunability, we have achieved a highly effective sorting of a particle mixture into three subpopulations based on the particle size, i.e., small, intermediate and large subpopulations. We even demonstrate the controllable tunability among three separation thresholds for elasto-inertial particle sorting without changing the geometry and dimensions of the microfluidic device. The tunability of the developed elasto-inertial particle focusing and sorting can significantly broaden its application in a variety of biomedical research studies.