How to register a theme function from the theme

I want to introduce a custom theme function in my theme. Typically, I would register a theme in hook_theme() in a module, but I want to define this function from my theme (Omega 4). In whatever module I'm in, I'd like to just build my render array and let it be themed by the theme-side theme function.

Example:

$ra = array( '#theme' => 'my_theme_fx', '#somevar' => 'foo', '#anothervar' => 'bar' );