Yep, it's called rapport in some cirlces. If you match the other persons tone, tempo and volume of voice, the tilt of their head, their posture, breathing rate and any sensory words (visual, auditory, feelings etc) they use then you kind of become like them or enter a similar state to them
People like poeple who are like them so this goes a long way to creating a trusting atmosphere.
I wouldn't recommend doing all these things at once as you will probably get caught but you can play around with it.
You will probably do this automatically with people you get on with really well.
Don't try and stop it if you notice yourself doing it as this is a completely normal process and one of the main ingredients to becoming a good communicator.
If you want to know more about this:
http://www.renewal.ca/nlp15.htm