You could update \CorrectChoice to insert an incremental \label. However, this would mean that only the most recent \CorrectChoice would be returned through a \theCorrectChoice call:

\documentclass{exam}% http://ctan.org/pkg/exam
\newcounter{correctchoicemark}% Counter to keep track of correct choice mark
\newcommand{\theCorrectChoice}{\ref{correctchoice-\thecorrectchoicemark}}% Print correct choice
\renewcommand{\choiceshook}{% Adapt \CorrectChoice to insert \label
\let\oldCorrectChoice\CorrectChoice% Store \CorrectChoice in \oldCorrectChoice
\renewcommand{\CorrectChoice}{%
\oldCorrectChoice% Original \CorrectChoice
\stepcounter{correctchoicemark}% Increment correct choice mark
\label{correctchoice-\thecorrectchoicemark}% \label original \CorrectChoice
}%
}
\let\oldoneparchoices\oneparchoices
\renewcommand{\oneparchoices}{%
\oldoneparchoices% Original oneparchoices environment start
\let\oldCorrectChoice\CorrectChoice% Store \CorrectChoice in \oldCorrectChoice
\renewcommand{\CorrectChoice}{%
\oldCorrectChoice% Original \CorrectChoice
\stepcounter{correctchoicemark}% Increment correct choice mark
\label{correctchoice-\thecorrectchoicemark}% \label original \CorrectChoice
}%
}
\begin{document}
\begin{questions}
\question This is a multiple choice question
\begin{choices}
\choice this is a choice
\choice this is another choice
\CorrectChoice this is the correct choice
\choice this is another choice
\end{choices}
The answer is \theCorrectChoice.
\question This is a multiple choice question
\begin{oneparchoices}
\choice this is a choice
\CorrectChoice this is another choice
\choice this is the correct choice
\choice this is another choice
\end{oneparchoices}
The answer is \theCorrectChoice.
\end{questions}
\end{document}
exam provides a hook into the choices environment via \choiceshook. Updating this to redefine \CorrectChoice is one (clean) way of inserting the appropriate code to obtain a \label you can \reference. oneparchoices does not provide this hook, so a different method altogether is employed in order to redefine \CorrectChoice.
More work is required for this solution to work correctly with hyperref.