I hope that I understand what you are saying correctly, but no, you can not unscrew it to reposition it.
No matter where you mount it, east needs to point toward the east, north toward north etc otherwise your wind directions will be wrong. Use a fascia mounted tv aerial pipe and then you can rotate your anemometer around it to align it correctly.
click
here and go to the setup page to see what I mean.
I apologise in advance if I have misunderstood you.