Just making a freely rotating joint is not that hard—consider a wheel—though the only biological examples are extremely tiny. What makes this complicated is that there are several independent systems that use the neck:

• Food in
• Air in and out
• Blood in
• Blood out
• Nervous system

The first four are tricky, but not so bad. You could set up some kind of a four channel coaxial rotating joint. [2] Kind of like four concentric pipe sections. There would need to be rotating seals, which would be tricky, especially to make biologically, but I bet you could do it.

The nervous system, however, is much harder. If you imagine cutting the neck at some height, there are a huge number of electrical connections crossing the boundary. While in theory this can be dealt with by the same coaxial approach, made somewhat easier because you have electrical and not liquid connections, this is just way too many connections to be workable. I think you would have to have a single high bandwidth serial connection over which you would multiplex the nervous system. You'd need a box at each end to connect up to all the nerves, which would be very difficult. And you'd need this all to be fast enough that the owl didn't feel delay in operating their limbs. This might be beyond what's even theoretically possible for information transfer.

So: if you were willing to put a lot of work into it, with extensive research to develop biological coaxial rotating joints and muxers, you might be able to make a freely rotating owl head. It might be easier to make a fully artificial owl, however.

[1] Probably a cached thought from childhood.

[2] If I understand it correctly, this is a two-channel non-biological one.