Assuming that you have a loop within your author.php file, grab the required metadata for every post within it, add it into a variable and display that after the loop has finished:
$author_vote_count = 0; //declare vote count variable before the loop
<?php while ( have_posts() ) : the_post(); ?>
// the stuff going on in your loop already
<?php if ( get_post_meta($post->ID, 'votes', true) ) {
$author_vote_count = $author_vote_count + get_post_meta($post->ID, 'votes', true);
} ?>
<?php endwhile; ?>
<?php echo "Total votes on author's posts: " . $author_vote_count; ?>
The above will only work as expected, if the meta_value of the key votes is an integer (or any type of number). Should it be saved in the database as a string, you need to convert it to an integer first. In that case use
$author_vote_count = $author_vote_count + intval( get_post_meta($post->ID, 'votes', true) );
instead.