Yes, you can claim your adult child who receives SSI as long as he meets the qualifications to be a qualifying relative. SSI is exempt from tax and does not count as gross income.
To claim someone as a qualifying relative:
They don't have to be related to you (despite the name)
They aren't claimed as a dependent by someone else
They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident
They aren’t filing a joint return with their spouse