Add category attribute to custom shortcode

add_shortcode( 'faq', 'wpse105856_shortcode_callback' );

function wpse105856_shortcode_callback( $atts ) {
    extract( shortcode_atts( array(
        'category' => ''
    ), $atts ) );

    $args = array(
        'numberposts' => -1,
        'orderby' => 'menu_order',
        'order' => 'ASC',
        'post_type' => 'faq'
    ));

    if ( ! empty( $category ) ) {
        $args['category_name'] = $category;
    }

    $posts = get_posts( $args );

    $faq  = '<div id="faq-accordion">'; //Open the container
    foreach ( $posts as $post ) { // Generate the markup for each Question
        $faq .= sprintf(('<h3><a href="">%1$s</a></h3><div>%2$s</div>'),
            $post->post_title,
            wpautop($post->post_content)
        );
    }
    $faq .= '</div>'; //Close the container

    return $faq; //Return the HTML.
});

Note: Even though the WP_Query parameter is called category_name, it expects to be given a slug.