So, you added something like:
array( 'url' => of_get_option( 'social_vine', '' ), 'icon' => 'fa-vine', 'title' => esc_html__( 'Follow me on Vine', 'quark' ) ),
In your functions.php, before the last one, which is the RSS?
Also, your options.php needs to have a corresponding area for vine too.
Enter this before the options array for the RSS in your options.php
$options = array(
'name' => esc_html__( 'Vine', 'quark' ),
'desc' => esc_html__( 'Enter your Vine URL.', 'quark' ),
'id' => 'social_vine',
'std' => '',
'type' => 'text' );
Just in case, make sure your font awesome files (CSS and fonts) are updated to the 4.1 which was when Vine was added - http://fortawesome.github.io/Font-Awesome/whats-new/