OK. Let's look at some numbers. Please feel free to correct me if I have made any grievous errors.

Assume your rods are 1 foot x 20 foot cylinders of pure tungsten.
Therefore each rod = 15.7 cubic feet = 0.44 cubic meters (approx).
The density of tungsten = 19,250 kg per cubic meter.
Each rod then has a mass of around 8,500 kg's. The 100 rods you want in orbit will have a mass of 850,000 kg's.

The most powerful rocket in the current US inventory is the Boeing Delta IV Heavy. According to Boeing, it has the capability to loft a bit less than 22,000 kg into low earth orbit. In order to deploy your payload, you would need the equivalent of 39 launches. Each launch costs about $300 million. Thus your total program costs (just to LAUNCH it) will run somewhere around $11.7 BILLION.

And this is a cost effective means to do what now?

How exactly would this be any better than taking a Minuteman III, removing the nuclear warhead(s) and replacing them with a chunk of, ... oh I don't know .... tungsten?

Personally I'd stick with our tried and true methods, which according to you only require a couple hundred thousand a pop.

So the real answer to the original question: Is there any way to stop Rods from God? Why yes, it's called fiscal responsibility.