Mathematically, alternating current and simple harmonic motion are described by essentially the same equations. You can draw some excellent analogies between a circuit with an inductor, capacitor, and resistor (which experiences an alternating current), and a damped mass on a spring. It's a good insight to see how they are alike.
However, I wouldn't say that AC current is actually an example of simple harmonic motion, as there isn't really any motion to speak of.
