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Yes - it is possible - but shares should be held in the custodial account - and you may form a business structure to accomplish self-directed IRA - see for instance - http://www.selfdirectedira.org/index.php/how-it-works
In connection with S-corporation in your question - only physical persons may be shareholders - so for your might need to change your business entity to LLC or C-corporation.
Please let me know if you need any clarification.