It's a common misconception that Google just scans your site and you automagically show up in searches. This is not quite the case, especially with a WordPress website.
Site rankings are made due to a variety of different variables. There's a lot you have to do on your end as well. If you haven't submitted a site map to Google, for example, you'll want to do that. You'll also want to make sure your pages are all SEO ready as well, with proper keywords and meta-descriptions.
There are some great plugins out there that can help with this. Some are free and some are paid. Do a bit of research and find the right one. That should help you tremendously.
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In addition I often recommend to get a free Google Webmaster Tools account so you can check exactly how Google sees your website.