A mathematical study is conducted of the oscillatory hydromagnetic flow of a viscous, incompressible, electrically conducting, non-Newtonian bio-fluid in an inclined, rotating channel with nonconducting walls, incorporating couple stress effects. The constitutive equations for a couple-stress fluid and the Maxwell electromagnetic field equations are presented and then reduced to a set of coupled partial differential equations for the primary and secondary flow. The model is then nondimensionalized with appropriate variables and shown to be controlled by the inverse Ekman number (K² = 1/Ek), the hydromagnetic body force parameter (M), channel inclination (α), Grashof number (Gr), Prandtl number (Pr), oscillation frequency (ω), and time variable (ωT). Analytical solutions are derived using complex variables. The influence of the governing parameters on the primary velocity (u), secondary velocity (w), temperature (θ), primary and secondary flow discharges per unit depth in the channel (Q_x, Q_z), and frictional shear stresses due to primary and secondary flow (τ_x, τ_z), are studied graphically and using tables. Applications of the study arise in the simulation of the manufacture of electrically conducting bio-polymeric liquids and magneto-physiological flow devices.