Since February 2016, you can add / create / upload new files from the GitHub web interface .
See " Uploading files to your repositories :
You can click the "Upload Files" button on the toolbar at the top of the file tree.

Or you can drag and drop files from your desktop into the file tree.

This replaces the creation of the file described in the answer of 2012 , and adds the ability to upload (for one or more files).
Original answer (March 2015)
The only part of the GitHub web interface that allows you to click on the binary (or any other file you want) when the release is created .
Then you can drag any binaries you need:

But for a regular repo, when creating new files , you can only edit a new file, not drag & drop the existing binary content:

So for now this is not possible (March 2015)
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