Current WordPress Page Title as Search Parameter into A Tag

Your shortcode is getting the title, but you haven’t told it to return anything, so a small tweak should fix things:

<?php
function post_title_shortcode(){
    return get_the_title();
}
add_shortcode('post_title','post_title_shortcode');
?>

You could also continue setting get_the_title() to $variable and add a line to return $variable, but the above is the simplest, shortest option.