Can a 230 volt 3 phase motor be connected to a 277 volt 3 phase circuit?

Only if you want to damage it.

"277" Volt 3-phase will usually mean 277 from each phase to neutral, and 480 from phase to phase.

By "230 3-phase", you likely mean 120 phase-to-neutral, and 208 phase-to-phase.

If you really mean 230, then you are probably NOT talking about a three phase motor.