Is an IRA Loan Allowed?
No. IRS rules dictate what you can do with IRAs and only allow 'distributions' from an account.
If you want to review the rules governing your account, check with the IRS or a tax advisor about taking an IRA loan or using another type of retirement account. Some guidance from the IRS is available here.
Alternatives to IRA Loans
Since you can’t do an IRA loan, you’ll have to try an alternative. You may be able to tap IRA assets using a 60 day rollover. You have to follow some strict IRS rules, but this technique can look like a short term IRA loan.
You might also be able to borrow against balances in company retirement plans such as 401(k) plans. Your plan must allow loans (not all of them do), and you’re taking a few risks -- including defaulting on the loan resulting in taxes and penalties. Work with your HR department and tax advisor to understand this technique.
Finally, you might try to borrow elsewhere. An unsecured loan (where your retirement savings are not collateral) may do the trick. Peer to peer lending services, family members, and banks or credit unions are also good options.
Investing in a Business
If you want to use assets in your IRA to invest in a business, you might be able to pull it off -- but it's not easy. Technically you won't borrow from the IRA. Instead, you'll set up an entity, fund it with the savings in your IRA, and use that entity for business purposes. The process is extremely complicated and you should definitely discuss the strategy with a CPA before you go too far.
This isn't something you can do with the standard IRA that you open at your bank or credit union; you'll need to work with a firm that specializes in using IRAs to invest in businesses. If you go this route, expect to pay at least several thousand dollars to get set up, and you'll have to pay annual fees as well.
Of course, it's worth a reminder here that most startup businesses fail. If you use your IRA, you risk losing your nest egg.