How do you build up a credit history with your spouse (non- US citizen)?

Add you on all the credit he already has and in the meantime any credit he applies for in the future have you on there as the co-borrower. You can also build your credit with a prepaid Mastercard/Visa. You can get one on this site. www.vrtmg.com/rlunsford just hit prepaid card and will tell you all the advantages of having a prepaid card.