Wordpress - add span class inside wp_nav_menu link anchor tag

Have you tried using the before or link_before parameters in your array arguments when declaring your wp_nav_menu function?

Note: use after or link_after for the opposite effect.

Example,

wp_nav_menu(

    //normal arguments here....etc

    'before'    => '<span class="arrow"></span>',

    //or 'link_before' => '<span class="arrow"></span>',


); 

From the Codex:

$before
(string) (optional) Output text before the of the link
Default: None

   e.g. 'before'    => ''

or...

$link_before
(string) (optional) Output text before the link text
Default: None

   e.g. 'link_before'    => ''

Supporting resources:

http://codex.wordpress.org/Function_Reference/wp_nav_menu


This actually creates two instances where it displays a span class within the tag on the primary and secondary levels so you can add different images to your span class for designing and navigating purposes.

This helps for users and developers to show if there is a drop-down to your header menu and also makes it easier to navigate within your website.

1. Add this code below to your functions.php first.

class Nav_Walker_Nav_Menu extends Walker_Nav_Menu {
     function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
        global $wp_query;
        $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

        $class_names = '';

        $classes = empty( $item->classes ) ? array() : (array) $item->classes;
        $classes[] = 'menu-item-' . $item->ID;

        $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
        $class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';

        $id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
        $id = $id ? ' id="' . esc_attr( $id ) . '"' : '';

        $output .= $indent . '<li' . $id . $class_names .'>';

        $attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
        $attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
        $attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
        $attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';

        $item_output = $args->before;
        $item_output .= '<a'. $attributes .'>';
        $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;

        if ( 'primary' == $args->theme_location ) {
            $submenus = 0 == $depth || 1 == $depth ? get_posts( array( 'post_type' => 'nav_menu_item', 'numberposts' => 1, 'meta_query' => array( array( 'key' => '_menu_item_menu_item_parent', 'value' => $item->ID, 'fields' => 'ids' ) ) ) ) : false;
            $item_output .= ! empty( $submenus ) ? ( 0 == $depth ? '<span class="arrow"></span>' : '<span class="sub-arrow"></span>' ) : '';
        }
        $item_output .= '</a>';
        $item_output .= $args->after;

        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    }
}

2. Add code below to your header.php where your wp_nav_menu is installed.

Explained below is the code so it installs the new custom menu in this case would be Nav_Walker_Nav_Menu.

<?php wp_nav_menu( array( 'container_class' => 'menu-header', 'theme_location' => 'primary', 'walker' => new Nav_Walker_Nav_Menu() ) ); ?>

3. Add some CSS

So it is able to show your new span arrow images within your tags in primary and secondary level.

#menu-header-menu li span.arrow { height:12px;background-image: url("images/nav-arrows.png");background-position: -8px -3px;background-repeat: no-repeat;float: right;margin: 0 0px 0 10px;text-indent: -9999px;width: 12px;}
#menu-header-menu li a:hover span.arrow{ height:12px;background-image: url("images/nav-arrows.png");background-position: -39px -3px;background-repeat: no-repeat;float: right;margin: 0 0px 0 10px;text-indent: -9999px;width: 12px;}
#menu-header-menu ul.sub-menu li span.sub-arrow { height:12px;background-image: url("images/nav-arrows.png");background-position: -8px -39px;background-repeat: no-repeat;float: right;margin: -2px 0px 0 10px;text-indent: -9999px;width: 12px;}
#menu-header-menu ul.sub-menu li a:hover span.sub-arrow{ height:12px;background-image: url("images/nav-arrows.png");background-position: -39px -39px;background-repeat: no-repeat;float: right;margin: -2px 0px 0 10px;text-indent: -9999px;width: 12px;}

hope this help! :)