Sure, people have been hunting elephants with bows and arrows since they were invented thousands of years ago.

With a bow of proper poundage (100+ pounds), an incredibly heavy arrow (1000+ grains), a very sharp and rugged fixed two blade broadhead (German Kinetics), and nerves of steel one could successfully harvest anything on this planet with a bow and arrow.

http://www.african-hunter.com/single_arrow_elephant.htm