Moved to ePO for faster response
There are a few pieces here you'd have to get set up.
1) You need to get Stinger uploaded into ePO as a package. (I haven't done this with Stinger specifically).
2) You need to create a Tag in ePO which will be applied to systems on which you want to run Stinger.
3) You need to create a Client Task in ePO and apply it to whichever ePO groups contain systems on which you will want to trigger Stinger executions. The task should be set to Run Immediately and should only apply to systems that have the tag you created in step 2.
4) On the Arcsight side, whenever you trigger a condition or correlation rule that would cause you to want to run Stinger, you trigger a call to ePO's Web API to apply the Stinger tag to the system in question. When the system next checks into ePO, it will receiver the Stinger task and execute Stinger.
I do not think that there is a Web API call to issue an Agent Wake-Up, which would allow you to trigger the Stinger execution faster, but if I'm wrong and you find otherwise, please let me know.
It's also useful to remember that you can use the ePO Endpoint Deployment Kit (EEDK) to create arbitrary packages and scripts, so you can use this method to do just about anything you'd like on the system.