This is a good guide to use Twitter in general, and also for Twitter as a research tool:
Tweet about each new publication, website update or new blog that the project completes. To gauge feedback, you could send a tweet that links to your research blog and ask your followers for their feedback and comments.
For tweeting to work well, always make sure that an open-web full version or summary of every publication, conference presentation or talk at an event is available online . . .
Tweet about new developments of interest from the project’s point of view, for instance, relevant government policy changes, think tank reports, or journal articles.
Use hashtags (#) to make your materials more visible – e.g. #phdchat. Don’t be afraid to start your own.
Twitter provides many opportunities for ‘crowd sourcing’ research activities across the sciences, social sciences, history and literature – by getting people to help with gathering information, making observations, undertaking data analysis, transcribing and editing documents – all done just for the love of it. Some researchers have also used Twitter to help ‘crowdsource’ research funding from interested public bodies.You can read more about crowdsourcing at the LSE Impact blog.Read it all . . .
See also this article on how Twitter will revolutionize academic research and teaching.