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