We want to pull LinkedIn profile text into our system. Does anyone know the API call which returns LinkedIn profile and perhaps could offer additional information which might make implementation easier?

Are you looking to push data into PCR? Perhaps a few more specifics about what you are planning to do will allow me to offer better guidance.

Pull the entire profile out into another system.

You are able to pull a candidates attachments which may contain something close to what you need. For example:

https://www2.pcrecruiter.net/rest/api/candidates/{CandidateId}/attachments

The above request would return the candidates attachments.