With the changes Twitter made to their API in early 2013, we can no longer use the Social Media module to embed a Twitter feed. However, there is still a way to do it! Twitter explains their Embedded Timelines feature here: https://dev.twitter.com/docs/embedded-timelines
To create an embedded timeline you must be signed in to twitter.com and visit the widgets section of your settings page. From this page you can see a list of the timelines you've configured and create new timelines.
Click the “Create new” button to build a new timeline for your website, choose the type, and complete the fields in the form; most fields are optional. The configuration is stored on Twitter's server, so once you've saved the timeline, a small piece of JavaScript code is generated to paste into your page, which will load the timeline. Copy this code to paste into your app.
Then, in your app dashboard, choose Mailing Lists and click Add Mailing List. (This isn't a mailing list, but really this module works for any embedded form.) Just give it whatever title you want to appear over your Twitter feed, and then paste the code into the box. Don't forget to set your Twitter icon on the right side before hitting Publish.
*For more information about how this works, how to embed multiple Twitter accounts in the same feed, or how to embed a hashtag feed, go to the Twitter page on Embedded Timelines here.