You can login with your Twitter credentials, to see the political leaning (between democratic and republican) inferred for you.
You can also search for other Twitter users and check their political leanings.
For a more detailed discussion of this work, please check out our paper:
Quantifying Search Bias: Investigating Sources of Bias for Political Searches in Social Media
20th Conference on Computer Supported Cooperative Work and Social Computing (CSCW'17). Portland, Oregon, USA, February 2017.