How can I attach a contact replying an email on Iphone with IOS7
You can send your Contact card via emai from the Contacts app.



The above was for Mac contacts, in your case for the iPhone there is a share contact with the same functions.

Share Contacts From Your iPhone Or iPad:

Open Contacts
Tap on a contact that you wish to share.
Scroll down and tap Share Contact.

You have three share options:

Airdrop (use only to share with other ios7)

Message

Mail

Choose the option you like, fill in the addressee details, and click Send.