How can admin generate invitation code, for new members registration and how can track members that signup with a particular code.
Is there any referral system in Social Engine?
I've moved this from the News and Announcements category as that's only for staff to post SocialEngine news.
You would need a third party plugin to track invitations and generate a code such as you want, or a customization. Otherwise, you could check the database for invitations sent out and use the front end invite feature to invite members from your admin account.
The below link includes a some info on iDevAffiliate which integrates with SE as a referral system. It's not a Plugin and I don't believe it does anything with the Invite Code. I only mention it because it's a true referral tool.
I second iDev as a viable option for what you are looking to do