Check with a prof or advisor to make sure you're not overestimating your own writing and waste a bunch of time first. If you get encouragement, there are graduate conferences for sure that sometimes accept undergraduate papers. I know the Borderlands graduate conference that happens every two years at UCSB occasionally takes an undergrad paper. Likewise if you were even more ambitious you could submit it to a professional conference. Again, work with an advisor to make sure you're not submitting something that gets accepted and then it turns out it's a huge embarrassment with your name attached. One grad student I know got a paper accepted at the APA without her advisor seeing it, and it turned into a huge deal because the advisor would not have allowed her to send that particular bomb anywhere if they knew about it.

That's not publishing, but it's the first step. Present your paper in public to other people who know something about it, get feedback, revise. I'm not sure about subsequent presentations of the same revised paper at later conferences; I've seen some people do that, but I've also been told it's bad form unless it's significantly revised to the point of being essentially new. Check again with your advisor.

If your paper is really good after revisions, there's no reason you can't submit it to an appropriate professional journal. The peer review there is super tough and so far 90% of my readers for a thing I'm trying to publish have been needlessly soul destroying in their comments.

There are often undergraduate journals or magazines universities put out. One I attended has an undergraduate law review. You might check around your campus to see what's around there.

What's the subject of the paper? I know of a few medieval history blogs that take submissions, but usually focused on very specific fields and prioritise grad students and lecturers over undergraduates. You might also want to consider publishing it yourself on your own blog or Medium account instead, if you can't find any blog willing to host it.

Two thoughts:

• A paper isn't "wasted" just because it stays unpublished. You wrote it for a specific purpose (learning, class requirement, etc.). It doesn't need to have more purpose than that. Those are quite enough. Experience with researching and structuring a 12 page paper is already quite a lot of non-wasted benefit.

• It is the rare undergraduate paper indeed that you probably want to have with your name on it out in the world forever. Just trust me on this, as someone who also thought very highly of his own undergraduate work, but has found that it ages ever more poorly over time. This is not to say that such work cannot be turned into something worth having other people see, but it likely requires a lot of editing, a lot of reading by other experts, and — perhaps — simply sitting on it for some time before it is worth that, given my experience with undergraduate paper (of which I have read literally thousands at this point, from a variety of different types of universities).

If you are going to keep working on such historical study, definitely don't publish undergraduate work right now. If you are not going to keep working on it, then there is even less incentive to think about what to do "next" with it.