As @Pyritium said, you should do something along that line. Something like this should work:
local Part = game.Workspace.Part -- Change part to your part name.
local oldOrientation = Vector3.new(Part.Orientation)
Part:GetPropertyChangedSignal("Orientation"):Connect(function()
local newOrientation =
newOrientation = Vector3.new(Part.Orientation)
print(tostring(newOrientation))
end)
Now I am not that experienced with Vectors, however if you have any problems, let me know!