Well, I could say that the answer completely depends on what production environment you are using
You can try out this new open source PMML "scoring engine" called Pattern, only if you are using Big Data on Hadoop
Else your only choice is to run R on server. You will save your fitted models in .RData files and then load them to run respective predict on the server.
This would be very slow but you can always try to use more hardware.
Now, how you do that completely depends on the platform. You can always use user defined function to add custom function in R.
Coming to Hadoop you can add such functions to Pig or you can use RHadoop to write simple map-reduce code to load the model and call predict in R.
If your data are in Hive, you can use Hive TRANSFORM to call external R script.
There are also other ways such as vendor-specific to add functions written in R to various SQL databases.