You can if you are the custodial parent, but there is no benefit to doing so (or even filing a tax return) unless you have taxable income. For example: unemployment comp is taxable, but is not earned income, so does not qualify for the EIC.
Child support is not taxable, so does not qualify for the EIC.
If there is another adult living in your household, he/she may be able to claim you and/or your son as dependents.
