Using Arduino to communicate with Atmega32 on L.E.D. Cube

Let me preface this by saying I don't have a whole lot of electronics or programming experience.

I have constructed an L.E.D. Cube using the following instructables (http://www.instructables.com/id/Led-Cube-8x8x8/?ALLSTEPS). I am currently trying to connect my PC directly to it (starts at step 63!) to do some more complex animations. The problem is, according to the instructions I need to modify an RS232 cable to use it, and non of my computers even have an RS232 connection. I was hoping I could use an arduino uno to go straight from its tx and rx pins to the respective pins on the Atmega32. Is this even possible? Would the code be complex? Any help or suggestions greatly appreciated!

Jon