Apple has some tools and methods you can use to find the Apple ID of an iPhone, BUT they can only be helpful for the original owner (Find the Apple ID of my Device).
The only method that can help you to find the iCloud ID/Apple ID of the original owner, which most of the times is the original owner’s e-mail address, is with the iCloud Contact Information Service. Not only it will provide you the Apple ID, but also all available contact information of him/her. Read more