Dear Student,
The direction of the magnetic lines of force is clockwise or anticlockwise depending on the direction of flow of current. So the direction of magnetic field can be obtained by drawing tangent to concentric circles at any point. By drawing tangents we see different directions of magnetic field at every point of circle but in all the cases magnetic field is also perpendicular to the direction of current.
So the magnetic field lines around the conductor is concentric circle perpendicular to the direction of current.
Regards