The electric current that travels through a wire produces an electromagnetic field around the wire.
The supposition that the wire tries to point north if an electric current passes through this wire, does not hold. If you place a compass near an wire and through this wire travels an electrical current, neither compass, nor wire, points the north. The only thing that can be observed is that the needle of compass points the direction of current flowing through the wire.
The direction of the magnetic field created around the wire is normal to the wire and it is given by the spin and orbits of electrons. You can determine the direction of magnetic field using the right hand rule.
Hence, if the current travles within a conductor, an weak electromagentic field is created around the conductor.