The following code will show week of the year number on the left side of the datepicker. By default the week start on Monday, but it can be customized using firstDay
option. The first week of the year contains the first Thursday of the year, following the ISO 8601 definition.
<input type="text" id="datepicker">
<script>
$("#datepicker").datepicker({
showWeek: true
});
</script>