The following custom Shortcode, will display a text imput field (with a submit button) where user can enter a coupon code to be applied.

Usage: [coupon_field] or in Php code echo do_shortcode("[coupon_field]");

The code:

add_shortcode( 'coupon_field', 'display_coupon_field' );
function display_coupon_field() {
    if( isset($_GET['coupon']) && isset($_GET['redeem-coupon']) ){
        if( $coupon = esc_attr($_GET['coupon']) ) {
            $applied = WC()->cart->apply_coupon($coupon);
        } else {
            $coupon = false;
        }

        $success = sprintf( __('Coupon "%s" Applied successfully.'), $coupon );
        $error   = __("This Coupon can't be applied");

        $message = isset($applied) && $applied ? $success : $error;
    }

    $output="';
}

Code goes on function.php file of your active child theme (or theme). Tested and works.

It displays a success or an error message, once applying a coupon.