The answer is NO.
Reason (adapt from http://invest-faq.com/articles/ret-plan-trad-ira.html)
The restriction comes from the combination of the following three facts. First, the law governing IRAs says that if any part of an IRA is used as collateral, the entire IRA is considered distributed and thus subject to income tax and penalties. Second, the rules imposed by the Federal Reserve Board et al. say that short sales have to take place in a margin account. Third and finally, margin accounts require that you pledge the account as collateral. So if you try to turn an IRA into a margin account, you'll void the IRA; but without a margin account, you can't sell short.