Betelgeuse is an example of a cool supergiant displaying brightness fluctuations and irregular surface structures. Simulations by Freytag, Steffen, & Dorch (2002) of the convective envelope of the star have shown that the fluctuations in the star's luminosity may be caused by giant cell convection. A related question regarding the nature of Betelgeuse and supergiants in general is whether these stars may be magnetically active. If so, that may in turn also contribute to their variability. By performing detailed numerical simulations, I find that both linear kinematic and non-linear dynamo action are possible and that the non-linear magnetic field saturates at a value somewhat below equipartition: in the linear regime there are two modes of dynamo action.