This is probably real basic.

I have a server with the foot file system with 6 GB alotted. I installed an application rpm with does not log to /var by default. As a result the root file system filled rapidly.

My question-- Is there any way to change a directory to a sym link to another directory on a partition with more storage? I think this may involve moving all the files and sub folders of the directory to another directory or partition. Then deleting that directory and creating a symlink. Move the files to the location the symlink points too.

Please correctd me where I'm going wrong.

yes, in general it is ok. But usually it should be a mount point, not a symbolic link.
and one more thing:
removing /var or /usr or /etc or a similar directory from a living OS will destroy it immediately, so you will not be able to complete this task. You would need to boot another OS (liveCD)