The effect of the magnetic shear on the current‐driven ion cyclotron instability has been studied. Taking into account the asymmetry introduced by the external current, an analytical theory to study the nonlocal behavior of this instability is given. The main consequences of the magnetic shear are to (i) localize the instability in space and (ii) reduce the growth rates in general. The damping influence of shear arises in two distinct ways; (a) a damping rate directly proportional to the shear strength, and (b) a damping rate (due to the nonlocal nature of the dispersion relation) not explicitly dependent on shear which can be quite strong for above marginal currents. Shear makes this instability more coherent by reducing the band of the perpendicular wavelengths which is unstable. The general physics of this instability and the parametric dependences of the growth rates are studied and marginal stability curves given.