These are two different questions. The answer to the first is “Yes.” If you are a student, it is not necessary to ask my permission to cite my blog. The blog is public, so you may cite it. Consult your teacher’s or professor’s preferred style guide on how to cite a blog.
However, if you are asked, as part of your assignment, to cite “scholarly” or “authoritative” or “peer-reviewed” sources, and you are asking whether you “should” cite my blog, that is not an easy question to answer. I noticed recently that my blog posts are appearing in library search results. This post seeks to provide a short cut to some of these complexities, by suggesting some contexts to consider. (That’s what scholars do, give you more to think about as a “short cut.”)
The reason that my blog posts, some of which I do not consider scholarly, are appearing in my university library’s search results is apparently because my library (or a library consortium of which it is a part) in late 2015 or early 2016 began purchasing access to the ACI: Scholarly Blog Index. “Ah, hah,” you reply, “so it is scholarly. Thanks for the short-cut. See-ya!” Hold on a second. Just because a scholar does something does not make what the scholar does scholarly. When I cook dinner, mow the lawn, shovel snow, etc., the fact of my doing those things does not make the doing of them scholarly. Same with my blog. Many things on my blog are about my area of scholarly expertise, but some things on my blog are not. The gold standard of “peer review” is that someone in a similar field reads it and approves it: my blog is not peer-reviewed. If I want to toss off a piece of snark, no one can prevent my publishing it here.
Why shouldn’t you let ACI: Scholarly Blog Index decide for you? Frankly, they seem a bit sketchy to me. They typically provide “descriptions” of blogs for you. No person is thinking while doing this: they’re just machine-scraping first several paragraphs. Libraries are paying subscription fees, but you cannot read the entire blog through their interface without paying them a per-use fee. That’s a great business model, but that’s not how scholarship ought to work. I am paid in part by public money (from state, though that amount is shrinking, and from occasional grants), so the products of my research ought to be free to public or, as much as possible, reasonably priced and in accordance with production costs.
The reason you’d pay ACI a fee is because you’re naive about fact that my blog is available also for free; because you are really impressed by their bells, whistles, or formatting; or because the original personal site by a scholar has disappeared from the Internet. Only the third reason is a good enough reason to cite ACI version, and even then try the WayBack Machine first. If a blog is publicly available, go to the publicly available site. Blogs may come and go, so there may be times it will be worth it to use ACI. But not often. If you read the “About Us” page of ACI, they’re a bunch of venture capitalists: they’re in it for the money.