Franklin Pierce University (US) a fully accredited university offers a minor in parapsychology with a major in psychology at the Bachelors level.
The University of Arizona (US) a fully accredited school has what amounts to a parapsychology lab (not department) under the direction of Dr. Gary Schwartz. I have provided a link below.
The medical school at the University of Virginia (US) another fully accredited school has what could be called a parapsychology lab (they call it Division of Perceptual Studies) under the direction of Dr. Bruce Greyson. I have included a link below.
So, no there is not a parapsychology department but there are fully accredited US universities that engage in the study of parapsychological topics.
No (they don’t have a unicorn department either, and for the same reason).
JFK University used to. However, they were the last. There is some other “colleges” that offer it, but they are not accredited.
Short and sweet answer: no, none at all. There’s a few universities in the UK that offer a degree but none in the US. It’s widely regarded as a pseudoscience.