How do I Assign Contacts to iCloud?
There are apps which let you manage the contacts (on device, icloud, etc) directly on the phone.  I've used the one linked below to do just that.  (Create a contact, and remember to copy it to the other side).  In the Contacts app, contacts which are in both the device (which is synced to the non-icloud computer) and icloud are shown as "unified info" when the data matches up, and at the bottom of the contact is a link to both cards.

https://itunes.apple.com/us/app/smart-merge-duplicate-contacts/id519076307?mt=8