How to call shortcode on button click

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>