Wordpress - Add custom classes to anchor in wp_nav_menu

You can do this with the nav_menu_link_attributes filter.

add_filter( 'nav_menu_link_attributes', 'wpse156165_menu_add_class', 10, 3 );

function wpse156165_menu_add_class( $atts, $item, $args ) {
    $class = 'class'; // or something based on $item
    $atts['class'] = $class;
    return $atts;
}

You can add classes natively via interface in admin. Open Screen Options (top right of the screen) and check CSS Classes. I don't remember if class applies to link itself, but you can always target link inside container with CSS (.class a).