It could be the alternator, but that is an expensive item. Before doing that, I would check all the battery connections and the ground straps that go from the engine to the body. Start with the battery terminal, make sure they are clean and tight.
Next, look at the - terminal of the battery. There are two cables from this terminal, the larger one goes to the engine block, the smaller one goes to a ground point next to the battery. Make sure both of these are tight and corrosion free.
At the front of the engine, next to the oil fill cap (4 cylinder model) is a small bolt with a small wire attached. This wire goes to one side of the front motor mount and then jumps to the other side of the motor mound. This is the secondary body to engine ground strap. It must also be clean and tight.
I would recommend undoing all the connections, clean up the surfaces with scotchbrite and reconnect them. See if the problem goes away. If it does not, then have the alternator tested for a ripple voltage in the output.