Could you charge a recharable battery with a voltaic cell?
Any source of electricity of the required voltage and current could be used to charge a rechargeable ("secondary") cell. A home-made "primary" cell would work (though you might need a few in series to provide the needed voltage).

For that matter, you can generate DC to charge the cell many other ways:


Using a thermopile, e.g. from copper and iron wire
Magnetohydrodynamically, e.g. with flowing salt water and a magnet
Using a photovoltaic panel...