How do I find out what is the minimum credit rating for a grad school loan (or undergrad) without a cosigner?

Private loans have the following criteria:

Most private student loans require a credit score of at least 650 on an 850 scale, though some lenders have much higher minimum credit scores. Borrowers with excellent credit scores may still be denied a private student loan because of secondary criteria, such as a high debt-service-to-income ratio (e.g., insufficient income or excessive debt), volatile annual income and self-employment.

Grad PLUS uses this:

The PLUS loan is the only federal education loan that considers the borrower's credit history. Eligibility does not depend on credit scores, but rather on whether the borrower has an adverse credit history. An adverse credit history is defined as having a derogatory event within the last 5 years (e.g., tax lien, bankruptcy, foreclosure, repossession, wage garnishment or default determination) or a current delinquency on any debt of 90 or more days.

References

• Quick Reference Guide on Choosing a Student or Parent Loan (pdf)

• Private Student Loans (pdf)

You could go to the bank that you're planning to borrow from and ask. There are two ways of checking loan eligibility: One is quick and does not affect your credit history, but the result is only approximate. The other is to do an actual loan application which will go on your history, but also produce an offer you can actually take. Depending on what you want, ask them to do one of these and see if you qualify. You can also go to a few different banks.

There is usually not a single cutoff for credit score, loan applications are evaluated based on many factors. For student loans, academic factors may also be considered. Exact details will vary with every loan, so you're better off asking either the bank, or the university's financial aid office.