Yes.Every individual who need a google adsense account may apply directly.I think rather than owning a website you need an email account preferably gmail account.Your own website may not be there or may not be easy to create.But you can create your own blog easily by logging to www.blogger.com.Remember that it is not easy now to get a adsense account.So you post some quality articles in your blog and try for adsense account continuously.