To create a new project with its own repository, do this. The svnadmin command assumes the path exists already:

$ svnadmin create /path/to/repository
$ svn import project_name file:///path/to/repository -m 'initial checkin'

Then remove the original copy and check it out:

$ mv project_name project_name.old
$ svn checkout file:///path/to/repository/trunk project_name

Note: You can change the file:// to svn:// or whatever protocol you're using.