<script type="text/javascript" src="https://code.jquery.com/jquery-1.10.2.min.js"></script>
<script type="text/javascript">
$(document).ready(function () {
    // Update this value to the number of links you want to show per row
    var numberOfLinksPerRow = 4;

    // local variables
    var pre = "<tr><td><div class='ms-promlink-body' id='promlink_row_";
    var post = "'></div></td></tr>";
    var numberOfLinksInCurrentRow = numberOfLinksPerRow;
    var currentRow = 1
    // find the number of promoted links we're displaying
    var numberOfPromotedLinks = $('.ms-promlink-body > .ms-tileview-tile-root').length;
    // if we have more links then we want in a row, let's continue
    if (numberOfPromotedLinks > numberOfLinksPerRow) {
        // we don't need the header anymore, no cycling through links
        $('.ms-promlink-root > .ms-promlink-header').empty();
        // let's iterate through all the links after the maximum displayed link
        for (i = numberOfLinksPerRow + 1; i <= numberOfPromotedLinks; i++) {
            // if we're reached the maximum number of links to show per row, add a new row
            // this happens the first time, with the values set initially
            if (numberOfLinksInCurrentRow == numberOfLinksPerRow) {
                // i just want the 2nd row to
                currentRow++;
                // create a new row of links
                $('.ms-promlink-root > table > tbody:last').append(pre + currentRow + post);
                // reset the number of links for the current row
                numberOfLinksInCurrentRow = 0;
            }
            // move the Nth (numberOfLinksPerRow + 1) div to the current table row
            $('#promlink_row_' + currentRow).append($('.ms-promlink-body > .ms-tileview-tile-root:eq(' + (numberOfLinksPerRow) + ')'));
            // increment the number of links in the current row
            numberOfLinksInCurrentRow++;
        }
    }
});
</script>