Is there any way to index my Github account to google search. I see that many people's account show up as soon as I type their name, but mine doesn't show up even after I type my name followed by github n search.
You can't force Google to index a page if it doesn't want to. You can suggest one to Google by using this link:
If you were an owner/administrator of the Github website you would have more options available to you by using Google Webmaster Tools