1/4" male compression end on inline water filter to 3/8" male compression (fine threads)
Since it seems that you already have the lines, I think all you need is a compression adapter fitting like this:

http://www.amazon.com/LASCO-17-6759-4-Inch-Compression-Adapter/dp/B008E5CFC4/

It will screw onto the female 3/8" compression on the drinking water faucet and allow you to connect a 1/4" compression line to it (from the filter).

This is one of the most commonly sold compression adapter at Home Depot, so anyone in plumbing should be able to point you to it (if you're in the US... I'm sure Lowes and others sell it to.  Quite common.