You can add the free Altmetric Bookmarklet to your browser and it will provide data such as the number of tweets and mentions for papers that you view on the web.
Altmetrics are alternative metrics, derived from the social web, for assessing academic publications. They can include tweets, mentions, bookmarks, downloads and followers. Altmetrics are much quicker to accumulate than bibliometrics and broader in scope because they can be applied to resources such as data sets, software and blogs as well as journal articles.
Some publishers display altmetric data on their websites and Altmetric and Plum Analytics badges are included in the University's Research Portal:
Altmetrics: A Manifesto is the document which first proposed altmetrics.