Found this on the WP plugin page:
<form action="https://YOURWEBSITE/wp-admin/admin-ajax.php" method="post">
<table class="acymailing_form">
<tr>
<td><label for="user_name">Name</label></td>
<td><input id="user_name" type="text" name="user[name]" value="" /></td>
</tr>
<tr>
<td><label for="user_email">E-mail</label></td>
<td><input id="user_email" type="text" name="user[email]" value="" /></td>
</tr>
<tr>
<td colspan="2" ><input class="button" type="submit" value="Subscribe" name="Submit" /></td>
</tr>
</table>
<input type="hidden" name="ctrl" value="frontusers"/>
<input type="hidden" name="task" value="subscribe"/>
<input type="hidden" name="page" value="acymailing_front"/>
<input type="hidden" name="action" value="acymailing_frontrouter"/>
<input type="hidden" name="noheader" value="1"/>
<input type="hidden" name="redirect" value="https://YOUR_REDIRECT_URL"/>
<input type="hidden" name="visiblelists" value=""/>
<input type="hidden" name="hiddenlists" value="YOUR_LISTS"/>
</form>