Yes, this is permissible but can be a little tricky. IRS rules regarding companies taxed as an S-Corporation are forbidden from having IRAs as owners. Investments into C-Corporations are certainly possible, as are investments into companies taxed as a partnership. However, if you or a disqualified person for your IRA (your spouse, lineal ascendants and descendants) are involved in the management of that private or start-up company, then there could be other prohibitions as well.
For more information on investing in a private or start-up company, please call us. We also encourage you to consult a financial professional (like an accountant or CPA) or see IRS Code 4975.