Could I buy a house with a credit score of 530 and an annual income of 25,000?

The minimum score for FHA is 580 now. Some lenders will go down to 540 with FHA financing but you will need a downpayment of 10-20 %

Good question: To be honest with you your income is not an issue as there are plenty of homes out there that would satisfy your income. The issue is how much debt do you carry as this will affect your debt to income ratio. Also your credit would need to be at least a 620 in order for you to get the rates and first time home buyer grants that are currently available. I would suggest getting with a credit repair specialist in your local area to find out why your score is so low.