Magento 1.9 – How to Call PHTML File into CMS Page Using Widget

Your phtml is rendered by a block class.
You need to add this in your block class.

protected $pageFactory;
protected $brandPage;
public function __construct(
    ....
    \Magento\Cms\Model\PageFactory $pageFactory,
    ....
){
    ....
    $this->pageFactory = $pageFactory;
    ....
}

public function getBrandsPageContent()
{
    if (is_null($this->brandPage)) {
        $this->brandPage = $this->pageFactory->create();
        $this->brandPage->load('brand_list', 'identifier');
    }
    return $this->brandPage->getContent();
}

then in your phtml you just call echo $this->getBrandsPageContent()

Add following code in your Block class, here Form class is an example

<?php
namespace Vendor\Module\Block;


class Form extends \Magento\Framework\View\Element\Template
{
    /**
     * @var \Magento\Cms\Model\Template\FilterProvider
     */
    protected $_filterProvider;

    /**
     * @var \Magento\Cms\Model\Page
     */
    protected $_page;

    /**
     * Store manager
     *
     * @var \Magento\Store\Model\StoreManagerInterface
     */
    protected $_storeManager;

    /**
     * Page factory
     *
     * @var \Magento\Cms\Model\PageFactory
     */
    protected $_pageFactory;

    /**
     * Construct
     *
     * @param \Magento\Framework\View\Element\Template\Context $context
     * @param \Magento\Cms\Model\Page $page
     * @param \Magento\Cms\Model\Template\FilterProvider $filterProvider
     * @param \Magento\Store\Model\StoreManagerInterface $storeManager
     * @param \Magento\Cms\Model\PageFactory $pageFactory
     * @param array $data
     */
    public function __construct(
        \Magento\Framework\View\Element\Template\Context $context,
        \Magento\Cms\Model\Page $page,
        \Magento\Cms\Model\Template\FilterProvider $filterProvider,
        \Magento\Store\Model\StoreManagerInterface $storeManager,
        \Magento\Cms\Model\PageFactory $pageFactory,
        array $data = []
    ) {
        parent::__construct($context, $data);

        $this->_filterProvider = $filterProvider;
        $this->_storeManager = $storeManager;
        $this->_pageFactory = $pageFactory;
    }

    /**
     * Retrieve Page instance
     *
     * @return \Magento\Cms\Model\Page
     */
    public function getPage($identifier)
    {
        if (!$this->hasData('page')) {
            /** @var \Magento\Cms\Model\Page $page */
            $page = $this->_pageFactory->create();
            $page->setStoreId($this->_storeManager->getStore()->getId())->load($identifier, 'identifier');
            $this->setData('page', $page);
        }
        return $this->getData('page');
    }

    public function getContent($identifier)
    {
        return $this->_filterProvider->getPageFilter()->filter($this->getPage($identifier)->getContent());
    }
}

Now you need to just following code for display cms page inside your corresponding phtml file

<?php echo $block->getContent('privacy-policy-cookie-restriction-mode');?>