Is it permissable for an IRA to invest in an S Corporation?

An IRA is permitted to own stock in a corporation. However, the S Corporation rules do not permit an IRA to be a shareholder, so if the IRA acquires stock, the corporation will cease to be an S Corporation.

Keep in mind that there are self dealing rules that would prohibit the IRA from owning stock in a corporation that you control. You also need a custodian willing to invest in a closely held corporation. Since the IRA has to be valued each year, most custodians won't go near it, and the ones that do will charge high fees.