Here are a couple of methods:
The code:
\documentclass[12pt]{exam}
\newcommand{\mycorrectchoice}[1]{\CorrectChoice \fbox{#1}}
\usepackage{tikz}
\usetikzlibrary{calc,shapes}
\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}
\newcommand{\DrawSmartBox}[1][red]{%
\tikz[overlay,remember picture]{
\draw[#1]
($(bl)+(-1.75em,1em)$) rectangle
($(br)+(0.2em,-0.4em)$);}
}
% \MyCorrectSmartChoice:
% #1 optional argument: aspect customization
% #2 mandatory argument: the answer
\newcommand{\MyCorrectSmartChoice}[2][black]{\CorrectChoice \tikzmark{bl}#2\tikzmark{br}\DrawSmartBox[#1]}
\begin{document}
\begin{questions}
\question Who is an idot?
\begin{choices}
\choice Not the writer of this post
\mycorrectchoice{The writter of this post}
\choice Who read this post
\end{choices}
\question Who is an idot?
\begin{choices}
\choice Not the writer of this post
\MyCorrectSmartChoice[thick,rounded corners,red]{The writter of this post}
\choice Who read this post
\end{choices}
\end{questions}
\end{document}
The result:

Notice that the example requires two compilation runs because of the \tikzmark macro; furthermore, this approach allows to customize the aspect of the box, as did in the example.