There are many people out there tweeting about graphic design. One minor problem in tweeting about something artistic is it is hard to represent a piece of design in a tweet, so almost all of those tweeting on the subject provide a link in their tweet to take you to the page that shows the designs. Not a huge issue, it is worth the trouble, but it takes just a bit longer. Here are some top tweeters:
Andrew Kelsall https://twitter.com/AndrewKelsall designs logos and other graphics. He is based out of the United Kingdom. Here is a tweet of his with a link (of course) that goes to a page showing excellent examples of design.
Jason Cass is a graphic designer, logo designer, and web designer from New York. He does something really cool; he tweets a logo of the day every day. Here is one:
(I know that you cannot see the logo in the tweet, he does not display them like that. But if you follow the link you will see some cool stuff)
Nicholas Patten takes a different approach to tweeting about design. While the others tweet mostly about great examples of design, Patten tweets about great resources for aspiring designers:
Despite what you may think about the tweeters I have listed, women tweet too! Veronica Domeier is a designer and she is also big on photography, an important part of design: