How can I replace the date picker with a text field that shows a date picker when it has the focus?

I installed the Date Picker module, which works fine. This is what appears when I add the datepicker element to the form.

This is the code I use to add the datepicker element.

$form['date'] = array(
  '#title' => t('Select your birthdate'),
  '#type' => 'datepicker',
  '#date_format' => 'd/m/Y',
  '#date_year_range' => '-100:+0',
  '#default_value' => date("Y-m-d H:i:s", time()),
);

I want to display a text field; when it has the focus, the calendar should be shown.

How should I change the code to make it possible?