Can you migrate my site from WordPress.com to my own self-hosted WordPress?

Yes, you can request for this service.

If you already had a blog on the WordPress.com platform you don’t have to start from scratch. We can migrate all your content including subscribers to your own self-hosted WordPress site with little to no loses to your current traffic.

Note: A site redirect subscription from WordPress.com is needed to redirect users if you were using their free WordPress domain (i.e yoursite.wordpress.com). Otherwise you’ll have to inform your old users of your new domain and may lose some direct traffic in the process.

It is however possible to redirect all the traffic from your currently indexed search engine results (Google and Bing) to the new domain.