You can’t add a shortcode to PHP directly. However, each shortcode executes a function, so you can just add that function to your link code.
If your shortcode is something like this:
function my_custom_shortcode( $atts, $content= NULL) {
shortcode function
}
add_shortcode ( 'my_custom_shortcode' , 'my_custom_shortcode' );
use this in your link:
<a href="https://wordpress.stackexchange.com/questions/253796/<?php my_custom_shortcode(); ?>" class="btn" > CLICK TO OPEN SHORTCODE</a>