Hello Rhyn,
Hm, this is going to be tricky because it's most likely that your "intro paragraph" contains html codes and you can't really wrap an anchor tag around a paragraph tag. It wouldn't work and I don't think that is semantically correct too.
If you really really need this, you got to modify the theme file which is located in /components/com_easyblog/themes/wireframe/blogs/latest/default.main.php and at line 157 locate the codes below:
<?php echo $post->getIntro();?>
Replacing it with,
<a href="<?php echo $post->getPermalink();?>"><?php echo strip_tags($post->getIntro());?></a>
P/S: There is already a continue reading button by default, wouldn't that be suffice?