Are adopted Chinese children citizens of the US?
Worf was adopted by a human family as a small child, I can't imagine by the time he's in his 40's he hasn't been granted Earth citizenship.
I don't think Worf was ever adopted. He was raised by Mr. and Mrs. Rozhenko, but I am sure he referred to them at different times as "Foster Parents" and "Parents"
AFAIK there was no formal adoption, which is why he refers to himself as "Son of Mogh" and not "Son of Sergey"
Nevertheless, to respond to the OP's question, I think Worf is a UFP citizen simply because he chose to be and he agreed to join Starfleet and adhere to their principles and rules of life.
He also retained his Klingon Empire citizen status when he wasn't blackballed.
He refers to them as "mother", "father" and "parents" in Family