I\'d like to retrieve the tweets for given a hashtag and sort them from the most retweeted to the less retweeted.
The closest thing I\'ve found is using the search call
This isn't a programmatic method but rather works in the browser with a chrome extension (HackyBird) :
P.S. It'll also sort your or any other user's timeline.
Results will sometimes contain a result_type field into the metadata with a value of either "recent" or "popular". Popular results are derived by an algorithm that Twitter computes, and up to 3 will appear in the default mixed mode that the Search API operates under. Popular results include another node in the metadata called recent_retweets. This field indicates how many retweets the Tweet has had.
Source (Emphasis are mine)
Just call with result_type=popular and check the recent_retweets
node to see how popular it is. result_type=popular
will become the default in an upcome release so beware if you omit this parameter.
Results with popular tweets aren't ordered chronologically. *
If you would like to always have results to show, use result_type=mixed: they will have the result_type
in the "metadata" section with a value of "recent", and popular results will have "popular". A small reference about result_types:
mixed: Include both popular and real time results in the response.
recent: return only the most recent results in the response
popular: return only the most popular results in the response.
If a search query has any popular results, those will be returned at the top, even if they are older than the other results. *
*[Twitter API Announcements]