Please follow below steps to assign order item value from the quote item.

step 1) Create a di.xml under app/code/Vendor/Module/etc/di.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <type name="MagentoQuoteModelQuoteItemToOrderItem">
        <plugin name="vendor_mymodule_sales_quote_item_order_item" type="VendorModulePluginSetOrderItemValue" />
    </type>    
</config>

step 2) Create the plugin file app/code/Vendor/Module/Plugin/SetOrderItemValue.php

<?php
namespace VendorModulePlugin;
use MagentoFrameworkSerializeSerializerInterface;

class SetOrderItemValue
{
    public function aroundConvert(MagentoQuoteModelQuoteItemToOrderItem $subject, callable $proceed, $quoteItem, $data)
    {
        $orderItem = $proceed($quoteItem, $data);
        $quotecustomattribute = $quoteItem->getMyCustomAttribite();
        $orderItem->setMyCustomAttribite($quotecustomattribute);
        return $orderItem;
    }
}