Federal Tax Laws do not consider the organ donation as a Charitable Deduction. If you file with an Itemized Deduction and you incurred Medical Expenses during the donation process you may include these expenses on your return. Keep in mind that Medical Expenses are only deductible if they exceed 10% of your AGI.
Additionally there are some States that offer Credits for Organ Donors. Please click on the link below to see if you live in one of these States and the benefits they offer: