Non-Newtonian droplet dynamics commonly exist in microfluidic systems. We report simulations of viscoelastic (VE) droplets traveling in a two dimensional capillary bifurcation channel. A numerical system combining phase field method, VE rheology, and Stokes flow equations is built. As a generic microfluidic two-phase problem, we study how a non-Newtonian droplet that approaches a channel bifurcation will behave. We identify conditions for when a droplet will either split into two or be directed into one of the branches. In particular, we study the importance of the non-Newtonian properties. Our results reveal two different non-Newtonian mechanisms that can enhance splitting and non-splitting of droplets with respect to Newtonian droplets, depending on the size of droplet and capillary number.