Get author total post votes from post meta

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.