Yes, you can:
add_action('wp_head',function() {
echo 'your html here';
});
However your .ico
file should be put in a place it can’t be purposely or accidentally deleted, like your theme folder beside your functions.php. Once done you can then use the following to construct the URL:
add_action('wp_head',function() {
echo '<link href="'.get_template_directory_uri().'/Buhehe.ico" rel="shortcut icon" type="image/x-icon">';
});
Note if you already have a shortcut icon
in the source code, the browser will pick whichever one its designed to pick (first or last).