Рабочий вариант:
<?php
$productId = '123';
$qty = '3';
$product = Mage::getModel('catalog/product')->load($productId);
$cart = Mage::getModel('checkout/cart');
$cart->init();
$cart->addProduct($product, array('qty' => $qty));
$cart->save();
Mage::getSingleton('checkout/session')->setCartWasUpdated(true);
?>