How to randomly categorize existing posts

I brought over more than 2000 daily short quotes/sayings from Blogger to my own WP site. There were never any categories, so my WP posts have no categories. I have a plug-in called Quick Featured Images that will create a featured image based on the category.

For example, I can assign rain-picture.jpg to every post that has a category of “1”, using this plug-in. And landscape.jpg can be assigned to every post with the category of “2”, and so on.

Is there a way (plug-in, etc.) to automatically give my existing posts a random category (1-20), thus allowing my Quick Featured Images plug-in to assign a featured image to each post?

Example where I have applied category 1 to existing posts, and had the plug-in update the post (except where a featured image already existed).
http://myvisiblesoul.com/category/1