I assume that you're looking for a career in academia? If so, the two most important things are to beef up your CV and to network.
For the CV, make sure that you publish as much as you can during your PhD. Don't wait until the end and publish one or two big manuscripts when you're almost done with the degree... be sure to publish throughout the 5 years that you're there, so that you can get your name out there. The higher the impact factor of the journal, the better. I'm in the biological sciences, so I don't know which journals are most "prestigious" in your field, but aim high (and if those journals don't accept your papers, just publish them elsewhere).
You can also beef up your CV by getting external funding awards. In my field, getting an NSF grant in your own name is a big deal, and definitely something that would make your CV look attractive. I'm sure that there are analogous awards in the political sciences that you can try for.
For networking, make sure to attend as many conferences as you can get funding for, even if you don't have anything to present at the moment. Use the time to introduce yourself to people in your field, who may have connections to other people at higher-ranking universities. Who knows... some of those people could end up being future collaborators of yours if you share common research interests! Of course, presenting your work (either as a talk or as a poster) at these conferences is preferable.
If you are going for a career in academia, then there's a good chance that you'll want to/need to do a postdoc between your PhD program and securing a job at a university. You could always try to do your postdoc at an institution with a higher rank? If you have a bunch of publications and conferences under your belt, there's a very decent chance that you can land such a position. You can also use the connections you made during your PhD to land a sweet postdoc.
At the end of the day, though, rank isn't everything. What really matters most is the quality of your work. Being at a lower ranking school just means that you may have to work slightly harder to attract attention to your work (that's where the publications and conferences come in), but if you're determined, you can do this. Good luck!
