The electromagnetic (EM) ion cyclotron (IC) instability of a plasma with parallel sheared current is investigated analytically with numerical solutions. This instability is the electromagnetic counterpart of the electrostatic current-driven ion cyclotron instability, which is renowned as the Drummond-Rosenbluth (DR) instability. Considered is the case with the current velocity shearing rate less than the ion cyclotron frequency, which corresponds to the tokamak and space plasmas. We found two new EM DR instabilities: the modified EM DR instability by the current shear and the subcritical EM DR instability which develops above the upper and below the lower critical velocities of the EM DR instability driven by the uniform current, respectively. The modified EM DR instability by the current shear develops due to the inverse electron Landau damping, whereas the subcritical EM DR instability develops due to the coupled effect of the IC damping and the current shear jointly with the inverse electron Landau damping. We also found the shear-flow-driven EM IC instability of the current-free sheared flow which develops by virtue of the coupled action of the IC damping and flow velocity shear.