I think that what you are looking for is a current source or a current mirror. These are active circuits that convey current to a circuit. I would advise looking at any book on transistors. You can build a current mirror BJT's or FETs. These are really low cost circuits. You pretty much just need two transistors, a resistor and your voltage source. The "art of electronics" is a good reference manual for all round electronics. Otherwise, you can use a search engine and look for something like "current mirror circuit diagram".
I think you can charge a battery like this. However, you should also bear in mind that there is something called compliance which means that the voltage of the circuit you are supplying (battery) should not rise above a certain level. This should also be explained in a book on transistors. Hope this helps ...