Yes indeed! Trim off the bottom leaves and stick it in rooting hormone, or just in a glass of water if you don't have the hormone. Works for me everytime! When you see roots, you can put it in ground or in a pot. You can even propagate the leaves! Here's a link for you:

and another link:
http://www.begonias.ca/prop_intro.htm

Here is a link that might be useful: propagating begonia leaves