The IRA can own an LP interest in a syndication. That part is straightforward: the account holds the limited partnership interest as its asset, and passive income from a real estate LP (distributions from rental income, your share of a sale) generally avoids UBIT, the "unrelated business income tax" that otherwise taxes certain retirement-account earnings.
The relationship question is the one that actually matters here, and I want to be direct: I cannot answer it for you, and neither can this forum. This is a tax and legal question that requires a licensed professional, specifically a tax attorney or CPA who specializes in SDIRA compliance, before you commit.
Here is why the question is live rather than settled. The prohibited-transaction rules disqualify transactions with "disqualified persons," which the code defines precisely: you, your spouse, lineal descendants, and entities you control above certain ownership thresholds. A GP you have a prior working relationship with does not automatically land in that category. But the IRS also looks at whether a transaction provides indirect personal benefit to the account holder, and "I sourced the deal" is exactly the kind of fact pattern a specialist needs to examine. The custodian will not catch this for you. The strategy guide is explicit on that point: custodians process transactions but do not police compliance, and the responsibility sits entirely with you.
One mechanical note: if this LP uses leverage at the fund level, the IRA's share of that debt can trigger UBIT on the income attributable to the borrowed portion, even though you borrowed nothing personally. Ask the GP for the fund's loan-to-equity structure before the conversation with your advisor.
What does the GP say about other IRA investors in the deal, and has the sponsor structured LP interests for SDIRA holders before?