The quasilinear intrinsic parallel flow drive including parallel residual stress, kinetic stress, cross Maxwell stress and parallel turbulent acceleration by electromagnetic ion temperature gradient (ITG) turbulence is calculated analytically using electromagnetic gyrokinetic theory. Both the kinetic stress and cross Maxwell stress also enter the mean parallel flow velocity equation via their divergence, as for the usual residual stress. The turbulent acceleration driven by ion pressure gradient along the total magnetic field (including equilibrium magnetic field and fluctuating radial magnetic field) cannot be written as a divergence of stress, and so should be treated as a local source/sink. All these terms can provide intrinsic parallel rotation drive. Electromagnetic effects reduce the non-resonant electrostatic stress force and even reverse it, but enhance the resonant stress force. Both the non-resonant and resonant turbulent acceleration terms are also enhanced by electromagnetic effects. The possible implications of our results for experimental observations are discussed.