  We determine the effect of a CPT-even and Lorentz violating non-minimal
coupling on the differential cross sections for some of the most important
tree-level processes in QED, namely, Compton and Bhabha scatterings, as well as
electron-positron annihilation. Experimental limits constraining the allowed
deviation of the differential cross sections relative to pure QED allow us to
place upper bounds on the Lorentz violating parameters. A constraint based on
the decay rate of para-positronium is also obtained.
