How to pull CID from inbound calls to integrate with POS system

Is there an easy way to do this? Meaning either a router, piece of software somewhere on the network, or even a box plugged inline with the phones that can pull the CID to feed into the ordering software (this is for a restaurant).

This particular credit card processor is Shift 4 and I’ve contacted them to see if they have an interest in doing some integration but if I can just pull the CID out and feed it to them that would enough.

How to feed it to them? Is it an API?

Pulling is done automatically. The question is how you communicate it to the external system. I don’t think you have provided enough detail to be sure of the best way of doing that