How do I index backlinks in Google? Is there any benefit?

Okay...

The answer to your questions is only get links from sites that Google already crawls.

You don't index backlinks in Google, Google indexes pages which have links embedded in the content.  Building baclinks is not for the novice.  You have to know how to vet a site before getting a link. 

The absolute quickest way to get Google to find new links to your site is get them from sites that Googlebot already visits.  

Submit Backlinks to Google Webmaster Tool, Ping the URLs, Make use of Social Networking Websites Use, Web 2.0

Backlinks are the bone of your Website and if they are not indexing properly, this clearly means they are not working anymore. For the very same reason, you have to focus on indexing your backlinks in Google faster. Here we have listed down the working solutions to index your backlinks in Google

• Submit Backlinks to Google Webmaster Tool
• Ping the URLs
• Make use of Social Networking Websites
• Use Web 2.0