You cannot claim a spouse as a dependent. You would file your return as Married Filing Jointly or Married Filing Separately. You would want to file as MFJ even if one spouse has little or no income. You receive the highest standard deduction and you each receive a personal exemption of $4,050.
If your spouse received Social Security Disability then that would be reported on your joint tax return. EIC is determined by earned income, adjusted gross income, filing status, age and dependent children (if any).
You can file a Form 8379 Injured Spouse Allocation with your joint tax return. The claim will prevent the IRS from seizing your portion of a tax refund for your spouse's debts.
See this TurboTax support FAQ for Form 8379 - https://ttlc.intuit.com/questions/1910698-how-do-i-file-form-8379-injured-spouse-allocation