If your incarcerated sibling does not meet the criteria mentioned by Champ @Mike9241 then, no, you cannot claim someone who is incarcerated as a dependent. In order to claim a dependent you have to provide over half their support----so their support (which even at the low end is well over $40,000 per year on average) is being paid for by the correctional facility and the tax dollars that pay to keep it in operation. Money you spend to provide for their incidental expenses, etc. is a gift, which is not deductible.