The linear response tensor for a relativistic counterpart of a bi-Maxwellian distribution is calculated in closed form for a magnetized plasma. The method used involves the following steps: (1) a covariant form of the response tensor for an arbitrary distribution of particles is derived using both a forward-scattering method and a covariant version of Vlasov theory; (2) the response tensor is evaluated for a strictly perpendicular, thermal distribution using a method due to Trubnikov; (3) the parallel distribution is built up by applying a Lorentz transformation to sum over a weighted, continuous distribution of parallel speeds. A convenient starting point for a detailed investigation of waves in such a plasma is the small-gyroradius approximation to the general expression for the response tensor, and the relevant approximation is derived and discussed briefly. The expansion of the general expression for the response tensor in Bessel functions in given in an appendix.