Mostly all of the docking software include pi-pi interactions but treat them as vdw interations. If you want to include true pi-X use more sophisticated scoring functions for example QM-Polarized Ligand Docking from Schrodinger - but this one should be time consuming.
This is by no means an extensive analysis of the subject, but I was curious to know this as well and I googled a bit.
This message about the AMBERff seems to be a good starting point. If you can access the forcefield parameters, you can see that most ring carbons have a slightly negative charge indeed. I also checked the forcefield that we use in HADDOCK and the atom type of ring carbons in tryptophan, despite having neutral charge, is that of a carbonyl carbon. In general, I would say this is represented by the ring having a slightly negative charge..
Nevertheless, from what I read, most potentials do not include this effect explicitly, and might fail at identifying it, or at least giving it its proper strength. As chupvl suggested, you will have to go to the QM level to accurately describe this. I found a paper comparing bit this effect in current forcefields, here.
The CHARMM forums might give more insight, but they are currently inaccessible..