try this...
<a id="signup-link" class="btn btn-primary" href="http://yoursite.com/login/signup.php"><i class="fa fa-sign-in"> Register</i></a>
Then add this to the Custom CSS box in Adaptable settings in ..
Administration > Site Administration > Themes > Adaptable > General settings or one of the many listed for Adaptable.
#signup-link { display: none;}
.notloggedin #signup-link { display: block;}
Then save the settings.
Actually there is nothing stopping you adding this to the Frontpage summary block
then move it to top right of the page.
Hope this helps?
Mary
EDIT: I've just edited this to fix some typos.