Hello there,
The answer is no.
Custom Design - Frequently Asked Questions
http://en.support.wordpress.com/custom-design/#frequently-asked-questions
On free hosted wordpress.COM blogs we can only use the themes which have been coded to run on this multi-user software and made available to us here. > Appearance > Themes and no others. We cannot edit either themes or templates on free hosted wordpress.COM blogs. > http://en.support.wordpress.com/themes/editing-themes/
If you wish to have complete control over a blog, the ability to upload themes and plugins, and to edit themes and templates then your option is to hire a web host and get a free software install from WordPress.ORG and self host it.
http://en.support.wordpress.com/com-vs-org/