Woo Auction Software supports the Escrow payments.
Steps for integration
Download the Escrow.com Payments for WooCommerce plugin from here.
Log in as the WordPress Admin of your website.
Navigate to Plugins > Add New to upload plugin.
Upload Escrow.com Payments for WooCommerce plugin.
Activate the plugin.
Go to Woocommerce > Settings > Payments > Escrow.com > Manage/Setup.
Enter your Escrow credentials and save the changes. To set up the Escrow credentials you can refer to official escrow plugin documentation here.