Is it possible to go from code to circuit?
Yes, it is certainly possible.
There are compilers that will compile from code to circuits.  Classic examples would be VHDL or AHDL compilers, but you can certainly do this for any other language, to the extent that you have an upper bound on the running time of the program or that you have an upper bound on the memory use of the program and are willing to have a circuit that contains stateful elements.
In fact, you can walk down to Fry's and buy something that basically has the form you asked for: it's called a computer.  That's more or less what a computer does: it takes code written in a programming language and executes it efficiently, using an optimized circuit.  The circuit is fixed (it is the gates in the processor) and part of its input is data that depends upon the program you are executing (which is stored in the RAM of the computer).  However, you could consider this a larger circuit where part of it is hardcoded (i.e., the program part of the input is hardcoded); then you can view a computer running a program as a big circuit with part that is universal and identical for all programs (the gates of the processor) and part that depends on the program (the hardcoded input), and this immediately gives a mapping from programs to circuits.  The mapping is implemented by a compiler.