A Turing machine is only a device to illustrate an abstract mathematical construct. Of course you can build a device that resembles a Turing machine, but usually they do not come with an infinite tape as in the original definition.

Another example of a real-world Turing machine can be found here: http://aturingmachine.com/

The infinite tape requirement is a bit difficult to fulfill, but that's true of the silicon implementations as well.