I assume TinyMCE will be stripping that tag because it is not valid in the body of the page. I believe it is not possible to set <link>
as a valid element in TinyMCE. As such, if you go to Extensions > Plugins and temporarily unpublish TinyMCE then you will be able to enter it using the blank editor.
If you do it this way, I'd suggest you add it to the page in a CustomHTML module and apply that to the page instead (this approach is only possible if the article is linked to a menu item), as saving the article using TinyMCE in future will always strip the tag.
If this does not work, press F12 and use your console to make sure the CSS is actually loading (it is unclear if you are loading it from your own site. If not, you may simply not be allowed to embed it.)
If it is on the page and loading correctly, make sure that your styles are being correctly overridden. It may just be that they aren't written in such a way that will take precident over your existing styles.
Finally, the best approach to adding such styles is probably in your template.
The following code will add a style sheet when the menu item id is 101.
<?php if (JFactory::getApplication()->getMenu()->getActive()->id=="101") {
JHtml::_('stylesheet', 'https://cdn.sstatic.net/Sites/stackoverflow/all.css', array());
} ?>
and the following will do the same when it detects an article of ID 1 (though if you are using other components, it may require additional validation to make sure the id belongs to com_content and not one of the other components)
<?php if (JFactory::getApplication()->input->get('id')=="1") {
JHtml::_('stylesheet', 'https://cdn.sstatic.net/Sites/stackoverflow/all.css', array());
} ?>
<style>
tags, not<script>
<link rel="stylesheet" type="text/css" href="https:"/>
- I updated my post to reflect.