The script thesacredpath mentioned is one possible way to get a link for a random image which you could then use in custom CSS that you write for your mobile theme.
To use that script, you would need to install it on an outside server where you are able to upload and execute PHP files, as thesacredpath suggested, and also upload a set of images in to the same folder where the script is saved or edit the $folder variable accordingly.
Once you had the script working and a set of images saved on an outside server, let's say the script URL is something like this:
Then you could use that URL to set it as the background in your custom CSS like this:
In order to do this, you do need to setup the script on your own on the outside server and get it working first.