You get the EIC on your tax return. You don't apply for it separately. When your prepare your tax return, first enter all of your personal information, including dependents, and enter all of your income. Then type EIC in the Search box and click the link that says "Jump to eic." TurboTax will ask a few questions to determine whether you are eligible for the EIC. If you are eligible it will include the EIC in your tax return.
