Hi Rarruga,
You could always add something like this to your header.php file:
<div class="alignright">
<?php get_search_form(); ?>
</div><!-- .alignright -->
But you may need to finagle with the styles in the header, particularly with the site-title and site-description tags (because they extend 100% of the way across the header space.
For example, I added the code above just below this section in header.php:
<hgroup>
<h1 class="site-title"><a href="<?php echo esc_url( home_url( '/' ) ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a></h1>
<h2 class="site-description"><?php bloginfo( 'description' ); ?></h2>
</hgroup>
And it looks sort of like this: https://cl.ly/image/0L2j433a3X40
Hope that helps.