Yes, you can use a self-directed IRA of your choice to invest in startups, provided they allow investments on the AngelList platform. Please discuss AngelList investing with your IRA provider prior to committing to an investment on AngelList.
At this time, self-directed IRAs are the only retirement accounts that we can accept as investment entities on the AngelList platform, so we do not currently support investing out of a 401k or other retirement account.