As Greg said, No. Each apps cookie storage is sandboxed.
A solution to the problem would be to use a SFSafariViewController, new to iOS9.
This implementation of WebViews are not sandboxed and have access to Safari's cookie storage. Meaning that two different apps could use this to both access the same cookies from Safari's cookie storage.
You would need to write a small web-service to handle writing the cookies and some sort of API to redirect cookie data back into the app.
Use this project as a starting point. It shows you how you can access Safari cookies from an app without the user having to do anything.
Hope this helps,
Liam