Your ssn can not be used for the Irrevocable Trust, since it needs its own identifier.
It is a bit unusual however that you are the trustee of an irrevocable trust which I assume you created. If you have any discretionary powers to control beneficial enjoyment of beneficiaries, the trust assets would still be taxable to you for estate tax purposes. That is why a third party is generally named trustee. So I am not sure why you are employing this type of trust.
If you are confused and the trust is in fact a "revocable" trust, then as it may be a "grantor trust" you could register it under your ss number.
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