Is there a link to GitHub for downloading a file in the latest release of a repository?

Linux solution to get latest release asset download link (works only if release has one asset only)

curl -s https://api.github.com/repos/boxbilling/boxbilling/releases/latest | grep browser_download_url | cut -d '"' -f 4

A few years late, but I just implemented a simple redirect to support https://github.com/USER/PROJECT/releases/latest/download/package.zip. That should redirected to the latest tagged package.zip release asset. Hope it's handy!

You can do an ajax request to get latest release download URL using the GitHub Releases API. It also shows when it was released and the download count:

function GetLatestReleaseInfo() {
  $.getJSON("https://api.github.com/repos/ShareX/ShareX/releases/latest").done(function(release) {
    var asset = release.assets[0];
    var downloadCount = 0;
    for (var i = 0; i < release.assets.length; i++) {
      downloadCount += release.assets[i].download_count;
    }
    var oneHour = 60 * 60 * 1000;
    var oneDay = 24 * oneHour;
    var dateDiff = new Date() - new Date(asset.updated_at);
    var timeAgo;
    if (dateDiff < oneDay) {
      timeAgo = (dateDiff / oneHour).toFixed(1) + " hours ago";
    } else {
      timeAgo = (dateDiff / oneDay).toFixed(1) + " days ago";
    }
    var releaseInfo = release.name + " was updated " + timeAgo + " and downloaded " + downloadCount.toLocaleString() + " times.";
    $(".download").attr("href", asset.browser_download_url);
    $(".release-info").text(releaseInfo);
    $(".release-info").fadeIn("slow");
  });
}

GetLatestReleaseInfo();

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<a class="download" href="https://github.com/ShareX/ShareX/releases/latest">Download</a>
<p class="release-info"></p>

It is important for you to set the default button URL to the releases page (like https://github.com/ShareX/ShareX/releases/latest) so if the browser does not support ajax (or javascript) or is too slow to get the URL, the download button will still work.

When the Ajax request completes, the URL of this button will change automatically to a direct download URL.

Edit:

I also made a downloads page that shows multiple releases which you can find here: https://getsharex.com/downloads/

Source code of it: https://github.com/ShareX/sharex.github.io/blob/master/js/downloads.js