Generally you can polish it out with a clean terrycloth towel and one of the Meguire's products. Meguire's has a whole line of various polishes from fairly agressive to very fine. Plus a line of various waxes. There are other brands, to be sure, but Meguire's is pretty easy to find.
Go into a local autobody supply store and ask the folks there. Make sure you get someone who's been there quite a while and knows what they're talking about. Or go talk to a reputable body shop. They'll steer you in the right direction.
I've had good success rubbing out these kinds of scratches, and worse. An electric buffer saves the arm if you have a lot. You will probably have good success making the scratch disappear, but if you look at the surface at an angle in the right light, you may still see a groove left by the branch in the clear coat. Thats just something you have to live with. Rewax the area when you're done. It's not hard, but it takes a little time and elbow grease. Chances are, you'll never notice it after that.
-Jay