How do you recycle a css file from a different theme into your new theme?
As @cilefen pointed out you need to do a couple of things.


Put the form.css on sites/all/themes/my_theme/css/. 
Update your sites/all/themes/my_theme/my_theme.info file to have stylesheets[all][] = css/form.css.
Clear the cache.


Oh and make sure that my_theme is set to default or at least active in the page that your are working.