When using our API you can currently request all networks except for Twitter. If you try to request Twitter data you will see the following warning: "This data source is not accessible via API. Learn more about why some data sources are not accessible via API here".
You'll also notice that in our API documentation we don't list Twitter. Because of Twitter's Terms of service, we can't allow access to Twitter data via our API. This is the sentence stated in Twitter's terms which we strictly oblige to:
"The best place to get Twitter Content is directly from Twitter. Consequently, we restrict the redistribution of Twitter Content to third parties. If you provide Twitter Content to third parties, including downloadable datasets or via an API, you may only distribute Tweet IDs, Direct Message IDs, and/or User IDs (except as described below). We also grant special permissions to academic researchers sharing Tweet IDs and User IDs for non-commercial research purposes. [...] In addition, all developers may provide up to 50,000 public Tweets Objects and/or User Objects to each person who uses your service on a daily basis if this is done via non-automated means (e.g., download of spreadsheets or PDFs)."
Please contact our Support team at firstname.lastname@example.org for further information.