It appears to be legitimate, with selection (as is usual for these honor societies) based entirely or almost entirely on your grades and class rank.
As to the value... it doesn't hurt overall, but it also won't help a lot either. This particular society appears to be limited to political science, so if you go outside of that field it becomes nearly worthless. Within the field, some will realize that it tells little about you beyond your GPA, others will recognize it but (being unfamiliar with the specifics) will think a little better of you for it, and some (being members themselves) will mentally up your standing as part of upping their own. A few will decide (correctly or not) that it is worthless and mentally downgrade you for taking part.
There are probably a few associated advantages to being a member - they might have a scholarship and fellowship pool for which you could compete, they might arrange special meetings with people from colleges or companies, or they might provide special opportunities to their members. Most members will not take advantage of them, and some will be national while others are chapter by chapter, but they are probably there. If nothing else, it is something else to put on your resume.
Bear in mind, however, that it is not one of the "big" honor societies that carry wide recognition or prestige - Phi Beta Kappa (humanities), Tau Beti Pi (engineering), Phi Kappa Phi (general). Is it worth $85? Maybe, that depends on how much you need the money, what your chapter has to offer, what you would make of it, and what else you have going for you.