If you have a backup archive files for your iPhone by iTunes created, you can also use iFoneMate for recovering iPhone contacts by iphone transfer iFoneMate in the same steps as recovery form device( check the post here).
Also you can use Apple��s iTunes to recover your iPhone contacts. First, you need to check you have backed up your iPhone Data to computer. If you have the backup data, you can follow these steps to retrieve your contacts.

Step 1: Run iTunes and connect your iPhone to the computer.
Step 2: Right-click your iPhone under the Devices list and click ��Restore from Backup��.
Step 3: Select the mobiletransf latest backup entry appearing under the most recent date and click ��Restore��.

Tips: Restore iPhone contacts from iTunes backup will erase all media tracks currently existing on your iPhone with the contents from the iOS backup files. If you are not willing to lose your existed contents on iPhone, iFoneMate would be your perfect solution to restore contacts from iTunes backup without erasing any of your previous data. that why we recommend you use iFoneMate to recover your contacts. try this great iPhone data recovery tool here.