Easy

If you have your IRA purchase real estate from an unrelated party and pay cash for it, and you do not use the real estate for personal reasons while it is in your IRA (i.e., you treat it strictly as an investment), there are no special issues.

More difficult

If your IRA invests in real estate through a down payment and leveraging, there are some significant issues:

1. You cannot personally guarantee a loan for your IRA;
   
2. It may be difficult to get a bank to allow an IRA to be the debtor without a personal guarantee. However, there are now some banks that specialize in loans to IRAs. Currently, the minimum IRA down payment for such loans is 30%, although the exact amount is up to the lender;
   
3. Your IRA will pay tax on UDFI (Unrelated Debt Financed Income), which is the income and/or capital gains attributable to the leveraged portion. (UDFI is taxed at the trust tax rate because an IRA is treated as a trust for this purpose.)

As a consequence, although it is perfectly legal, it may not be desirable to have an IRA carry debt in a real estate investment transaction if there is any significant risk that the IRA will be unable to pay the mortgage payments.