Custom Widget Shortcodes

/**
 * Enable Widget shortcodes.
 */
add_filter('widget_text', 'do_shortcode');

/**
 * Custom Widget Shortcode.
 */
add_shortcode('custom', 'custom_widget');   
function custom_widget($attr, $content) {        
   	ob_start();  
    get_template_part('inc/custom');  
    $ret = ob_get_contents();  
    ob_end_clean();  
    return $ret;      
}

Then in the widget just add [custom] and it should work.