On GitHub.com
The GitHub wiki site strips out the download attribute, so conventional approaches as mentioned before aren't going to work properly. However, I found the following will work:
<a id="raw-url" href="https://raw.githubusercontent.com/github-username/project/master/filename">Download FILE</a>
Replace 'github-username' with your git hub user name, obviously. Replace 'project' with project name, 'filename' with the actual file name. This also assumes the file is not in a sub folder. Also, notice, it is actually hosted on raw.githubusercontent.com.
However, due the difficulty, I'm almost wondering if the site was intentionally deterring such behavior.