can an ftp site "see" my MAC address?

Do MAC addresses (unique network card identifier) get transmitted over the internet when you connect to an ftp site, or does that info stay within your local network? Are there any internet protocols that transmit your MAC address?

Your MAC address does not travel outside your local ethernet under normal circumstances. There’s nothing to prevent a program from sharing that information over the Internet if it so chooses, but nothing in the FTP protocol does so. FTP predates Ethernet by quite a while.