Add JavaScript function to wordpress theme

You need to add the code to a javascript file and enqueue it in functions.php, or echo it via an action hook.

There's a section about including JavaScript right in the codex that's worth a read.

This is a Javascript function, not a PHP function. This means that you need to do the following:

<?php

// Your existing PHP code here

?>
<script>
  function WPACLoadMoreComments() {
  window.WPACLoadMoreCount = window.WPACLoadMoreCount || 1;
  var url = (new Uri(location.href)).replaceQueryParam('WPACTake', window.WPACLoadMoreCount * 20).toString();
  if (WPAC.LoadComments(url, {updateUrl: false})) {
    window.WPACLoadMoreCount++;
  }
}
</script>
<?php

//Your remaining PHP code

?> 

Another possibility is to do it this way:

<?php

echo "<script>";
echo "  function WPACLoadMoreComments() {";
echo "  window.WPACLoadMoreCount = window.WPACLoadMoreCount || 1;";
echo "var url = (new Uri(location.href)).replaceQueryParam('WPACTake', window.WPACLoadMoreCount * 20).toString();"
echo "  if (WPAC.LoadComments(url, {updateUrl: false})) {";
echo "    window.WPACLoadMoreCount++;";
echo "  }";
echo "}";
echo "</script>";

?> 

The reason we're doing it this way is that Javascript is not executed on the server but on the user's browser (client side). Thus, there is no need to put the Javascript in <?php ?> tags, because you do not want it to be executed as PHP code. Since it will be executed by the browser, this means you need this code to appear in the HTML document loaded by the browser, and hence you should use echo or write it within <script> tags outside the <?php ?>

Performance-wise, it is always better to put Javascript code at the end of your page. This is to make sure that any possible lags, caused by the JS code while a user's browser is loading your page, do not affect the rendering of the page.

Put it in the functions.php or footer.php file somewhere outside <?php ?> and wrap it into <script type="text/javascript">Your function here...</script>