  Magnetic fields have been measured recently in the core of red giant stars
thanks to their effects on stellar oscillation frequencies. The search for
magnetic signatures in pulsating stars, such as $\gamma$ Doradus or Slowly
Pulsation B stars, requires to adapt the formalism developed for the slowly
rotating red giants to rapidly rotating stars. We perform a theoretical
analysis of the effects of an arbitrary magnetic field on high radial order
gravity and Rossby modes in a rapidly rotating star. The magnetic effects are
treated as a perturbation. For high radial order modes, the contribution of the
radial component of the magnetic field is likely to dominate over the azimuthal
and latitudinal components. The rotation is taken into account through the
traditional approximation of rotation. General expressions of the frequency
shift induced by an arbitrary radial magnetic field are derived. Approximate
analytical forms are obtained in the high-order high-spin-parameter limits for
the modes most frequently observed in $\gamma$ Dor stars. We propose simple
methods to detect seismic magnetic signatures and measure possible magnetic
fields in such stars. These methods offer new possibilities to look for
internal magnetic fields in future observations, such as the ones of the PLATO
mission, or to revisit existing Kepler or TESS data.
