I am configuring the Sharepoint 2013 search and want to have the scopes in the search page, but as we all know, scopes are a deprecated feature in Sharepoint 2013. So my question is can we use result sources in Sharepoint 2013 search as a refiner? If so, how?
The way I understand Result Sources, they are the new Search Scopes. It's more a renaming thing, though there are subtle differences.
You may be mixing terms here. You wouldn't normally use a scope as a refiner, but perhaps have different results pages for different scopes, as you'll probably want the presentation of the results to vary.
Hopefully this answers the original question (though I have the same requirement but this does not solve my own problem for various reasons).
In 2013 "scopes" have been removed, but now you can change result sources on the Search page by using the Search Navigation webpart. You have to create a new results page for each one and the space on the webpart is limited so you should be very selective about which ones you add, but that's the new method for changing "scopes" on search results.
See this article for instructions on how it works.