function your_theme_user_contacts( $user_contactmethods, $user ) {
    $user_contactmethods['twitter'] = 'Twitter';
    return $user_contactmethods;
}
add_filter( 'user_contactmethods', 'your_theme_user_contacts', 10, 2 );

And to get this on the author archive page, for example, just use:

$twitter = get_the_author_meta( 'twitter' );