Not directly. The BoxCaster itself requires DHCP to access our media servers so assigning a static IP to the device itself will not work but you can handle this from the network side by adding the MAC ID (found on the bottom of the BoxCaster or in the sources area of the dashboard) to the DHCP server and then creating an IP reservation in your network for that MAC ID. This way, when your network sees the BoxCaster online it can give a specific IP, no problem.
There is also a work around if the above fails for you. Bear in mind that this isn't the recommended first option. You can plug the network into a router and then plug the router into your BoxCaster. You can assign a static IP to the router while still allowing the BoxCaster to request DHCP. It is never ideal to add an extra piece of equipment between the network and the BoxCaster as this increases the chance of latency but it can work in a pinch.
To find your Mac ID address of the BoxCaster, go to the sources tab and click on the BoxCaster.