Use the circle API to get the link to the latest build for a given project / branch

circle.html

<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<script>
    var url = new URL(window.location.href)
    var user = url.searchParams.get("user")
    var repo = url.searchParams.get("repo")
    var branch = url.searchParams.get("branch")
    var token = url.searchParams.get("token")

    var circleUrl = "https://circleci.com/api/v1.1/project/github/" + user + "/" + repo + "/tree/" + branch + "?circle-token=" + token

    $.getJSON(circleUrl, function( data ) {
        window.location.replace(data[0].build_url)
    });
</script>

If your project is private you'll need to generate a circle API token with artifact access and include it as a url param when hitting this page.