When a steady current flows through a long straight wire, the magnetic field lines form concentric circles around the wire, as per Ampere’s Law. The direction of the magnetic field lines follows the right-hand rule: if you curl the fingers of your right hand around the wire in the direction of the current, your thumb points in the direction of the magnetic field.
Therefore, for a vertical current-carrying wire, the magnetic field lines will be horizontal and form concentric circles around the wire.