This feature exists in the category list view, we are just transporting it over to the category blog view.

Create the normal override in your template (move blog.php from the com_content component to your html folder within your template) if you have not already done so, then copy/paste the following code into the file where you wish it to appear. In the past I have added some CSS to make a fixed floating tag at the side of the screen.

<?php // Code to add a link to submit an article. ?>
<?php if ($this->category->getParams()->get('access-create')) : ?>
  <?php echo JHtml::_('icon.create', $this->category, $this->category->params); ?>
<?php  endif; ?>

The result should only be seen by authorized and logged in users, that is, those with publishing privileges.