The usual approach would be to create links to the website from other prominent indexed websites. So for example, you might want to create a link to the page from your university profile page. You could also add links from ResearchGate, LinkedIn and other social networks that allow you to share a link to a personal website. You could start creating content and sharing it on social networks.
Then, you just have to wait a bit for the web crawlers (particularly Google) to find and index you. This might take a month or more.
If you are specifically interested in being indexed by Google Scholar, check out these guidelines:
If you're an individual author, it works best to simply upload your
paper to your website, e.g., www.example.edu/~professor/jpdr2009.pdf;
and add a link to it on your publications page, such as
www.example.edu/~professor/publications.html. Make sure that:
the full text of your paper is in a PDF file that ends with ".pdf",
the title of the paper appears in a large font on top of the first
page, the authors of the paper are listed right below the title on a
separate line, and there's a bibliography section titled, e.g.,
"References" or "Bibliography" at the end. That's it! Our search
robots should normally find your paper and include it in Google
Scholar within several weeks.
If it doesn't work, you could either (1) read more detailed technical
guidelines in this documentation or (2) check if your local
institutional repository is already configured for indexing in Google
Scholar, and upload your papers there.