We present an electrochemical method for the synthesis of iron hydroxide nanowires, together with a detailed structure and magnetic characterization. The nanowires are single crystalline and show the structure of goethite without traces of any other iron oxide or hydroxide. The nanowires are antiferromagnetic, like bulk goethite, but show a small magnetic hysteresis which arises from uncompensated surface spins. Exchange bias is also reported in the nanowires, an effect related to the coupling between the antiferromagnetic bulk and the surface spins, that shows weak ferromagnetism.