WP_Query
accepts a search parameter, ‘s’. Hence, you can just do this:
<?php $related_posts = new WP_Query( 's=" . the_title_attribute( "', '', 0 ) );
if( $related_posts->have_posts() ) : while( $related_posts->have_posts() ) : $related_posts->the_post();
// STUFF
endwhile; endif; wp_reset_postdata(); ?>
While we’re here, note the use of WP_Query
which is more appropriate for a secondary loop. You can also take a look at the link above if you want to add additional paramemters to restrict by post_type
or taxonomy or anything else.