How to share a contact card via iMessage using the iOS Contacts app
How to Add a contact card via after receiving it in A iMessage
1.Tap on the contact card.
2. The contact card will pop up. Scroll down
3. If you want to create a new contact with that card choose crate new contact.
Or to add it to a existing contact. Choose add to existing contact. And find the contact you want to add it to.