As of 2016 February you can use the new upload files feature.
You’ll soon be able to skip the command line and upload files directly to your repositories without having to leave the browser. Repository uploads will be rolling out over the next few days, so if you can’t upload yet, sit tight.
You can click the “Upload files” button in the toolbar at the top of the file tree.
Or, you can drag and drop files from your desktop onto the file tree.
Or, you can drag and drop files from your desktop onto the file tree.
[Gif file not supported by the SE upload.]
Once you’ve added all the files you want to upload, you can commit them directly to your default branch or create a new branch and open a pull request. This will look familiar if you’ve used the “New file” button before.
Source.