Go to settings/icloud on your phone. Make sure you are logged with your Apple ID.
Contacts should be on, click on it to turn it off and choose keep (even though you show no contacts)
When the process is done go ahead and turn on contacts again, choose merge. All your contacts should show up if you had a previous backup to icloud.
NOTE: You don't have to restore your phone.
more info at...
iCloud: Backup and restore overview