Can I promote my own website here?

Generally speaking, a certain level of self-promotion is OK here. In fact, here's an entire feature "Show HN" just for showing off your own stuff. But as a corollary to the guidelines[1] and FAQ[2] do say that HN is not primarily for self-promotion. And if all you post is just self-promotional content, and/or if you're posting self-promotional stuff all the time, it's going to be frowned upon and could result in your account being restricted or something.

From the guidelines doc:

Please don't use HN primarily for promotion. It's ok to post your own stuff part of the time, but the primary use of the site should be for curiosity.

[1]: https://news.ycombinator.com/newsguidelines.html

[2]: https://news.ycombinator.com/newsfaq.html

By promote your own website, do you mean the site / business, or your own articles etc?

People do a Show HN for their business or product often.

For articles / blogs, good question. I just posted -- one minute before I saw this in new! -- an article I wrote. I think it's interesting to the HN audience, so I posted it. Now I wonder if that's okay to do.

I'd say as long as the content that you're sharing is actual quality.