I have created a new game, can I announce my website here? Where can I go to get the word out? Thanks.
No, it isn't.
This is a Q&A site (see the tour), so anything you post needs to either be a specific question (i.e. not "do you like my game") or an answer to an existing question.
Additionally, unsolicited self-promotion is frowned upon, so it generally won't be appropriate to promote anything here. You're welcome to mention a game you've made if it's part of a direct answer to a question and you disclose your affiliation, but that's not something that comes up often; people tend to ask questions about existing games, and game recommendation questions are off-topic.
One thing you are allowed to do is put anything you like in your profile (as long as its not offensive). So you can put your website address in there, and as much blurb as you like about it.
Of course, people are unlikely to read your profile unless you post lots of high quality answers. Which is good, because we'd like you to become a member of the site, not just post something about your game and then disappear.