Unfortunately, we don't currently provide the ability to connect a custom segment to the dashboard. However, you CAN connect a custom view profile, which can often accomplish the same end results as a custom segment.
This article on the Google Analytics support site explains the step by step process for creating a view profile within your analytics account.
Once you've created the view profile, it will have it's own property ID, in the format of UA-xxxxx-xx. To connect it to our dashboard, follow these instructions for connecting a standard Google Analytics integration. When you get to the point of choosing an account to connect, select the one with the new property ID that you've just created.