You can find answer on the github support.

There are technical limitations, we tried this in the past and it had a negative impact on performance. If we find a solution, we'll re-implement it.

https://help.github.com/articles/getting-the-download-count-for-your-releases/

If you archive your project and post it as a download, you can see how many times that archive has been downloaded (e.g. https://github.com/jhclark/multeval/downloads).

However, I'm not aware of any way of doing this for downloads of the entire source tree.

You can also perform this programmatically by leveraging the GitHub API. There's a whole section dedicated to the Package Download API.

Below the syntax to retrieve the list of downloads

GET /repos/:user/:repo/downloads

For instance here are the list of downloads of the libgit2 project: