I understand paranormal activity to refer to things such as hauntings or extra-sensory perception, things that probably close to half (or more) of the population believes in firmly and another large portion of the population dismisses as hoax or superstition. With such disagreement, there's certainly material for a good persuasive essay.
Your argument could be either 1) the study of oaranormal activity has nothing nothing to do with science or 2) paranormal activity is a legitimate field of scientific study.
If I were writing the essay, I think I might focus on some specific "text" that deals with paranormal activity, such as an episode or two of "Ghost Hunters," a series that always seems to be airing on the SciFi channel whenever I'm in the mood to watch science fiction (rather than ghost hunting). My thesis might end up being something like this: "Although the supposed study of the paranormal in 'Ghost Hunters' claims to be scientific -- with thermal imaging technology, etc. -- the show presents something that is much more valuable as entertaintment than as scientific study."
To develop my argument, I might look at the ways in which the actors on the show (I'd argue in the essay that they're actors, not scientists) set the stage by telling some sort of background story about the place they're investigating, how they seem to latch onto any anomaly as evidence of "something," etc.