Solved: Can I only allow an IP Address on a specific MAC Address?

As others have mentioned. DHCP reservations and port-security are your best bet. I'd encourage you to configure both.

You can reserve the IP to MAC in your DHCP server but that does not stop somebody from statically assigning this IP address if they wanted.

Port security will only authenticate based on MAC address, there is nothing to stop that mac using a different IP address.

If you really wanted to go nuts you could assign on ACL and/or VACL to the port as well and look into some sort of 802.1x based authentication (but like others have said unless your in a hostile environment or work with state secrets this probably a little over kill).