That would probably be your best bet. Try to focus your lens about where you think the bird will be in frame where you take your shot. If you have a continuous shot setting (that will let your camera shoot several photos consecutively), that will also make it easier for you to capture the shot.
A problem you may be experiencing is motion blur because of how fast the parrot is moving. You can offset this problem by shooting at a fast shutter speed. Most digital cameras will set their shutter speed automatically, but you can try to force it to use its fastest setting by looking for a mode customized for sports. If not, you can also look into your camera's AE settings, and put it on shutter priority.
Hope that helps
