There are a few ways that I'm thinking that can solve your problem.
One is by resorting to a third party program which basically does what you want. It will encrypt anything that goes to Dropbox but requires a client to be installed on your system to be able to access your data.
http://www.pcworld.com/article/2046475/five-free-dropbox-tools-youre-not-using-but-should-be-.html
Another way is to write your own scripts to be enable you to do the same thing. The only thing here is that you need to watch for sub-standard encryption implementations, programs, etc... (though in this case I don't think that'll be too big of an issue?)
The final way is to use something like Sikuli or SuperMacro to achieve basically the same thing as scripting will achieve except in a graphical environment (more friendly for non-programmers)
http://www.sikuli.org/