Does Discord has an application that can be run on a Raspberry PI ? Their clients include mac/windows/linux (x86) or android, but I don't see anything for a system with ARM CPU.
As far as I know, RetroArch on PC/Mac/Linux has the possibility to interact with Discord, but in the end it needs to be properly integrated into RetroPie.
What are you thinking when you say 'integrating' ?
If it's already included in RetroArch, the you can configure it and you're good to go.