http://www.cesm.ucar.edu/models/ccsm4.0/ seems to offer what you are looking for (first Google hit for “NCAR climate model source code”) but without a cluster of supercomputing nodes, what are you planning to do with it?
ESCM is a smaller one and it seems there are transport matrix models which could be small enough for a single workstation?
Study it. Read the source. Maybe adapt it to a system that isnt a supercomputer. We'll see.
This is mentioned elsewhere in the comments at least some of the code for climateprediction.net appears to be on GitHub: https://github.com/CPDN-git.