It is only possible to take space from one partition and give it to another if the two partitions are adjacent to one another. There are tools available that are designed to modify partitions, such as Partition Magic or the one I prefer,
Boot IT, however, as I'm sure you're aware, making any sorts of changes to your partitions is an inherently risky move, especially if you're dealing with an important Production machine. Therefore, make backups before doing anything.
Apart from using a utility tool to modify your partitions, you could also drop and recreate them (which may not be practical) or if you've got an extra hard drive you can add to the machine, then you could transfer /var over to it. No matter what your choice though, the most important thing is to have a good set of backups in case anything goes awry. Good luck with the project. -- J.W.