Is it possible? Why not? I would like to star one for bookmarking. It is very much down below original question so it will be much easier to just star an answer.
There is currently no way of "starring" an answer that I know of (in the same way you can favorite a question). I just use a bookmarks folder in my toolbar and drag questions and answers to it. In this case, you can drag the "Share" link to your browser bookmarks toolbar or whichever place suits you.