The magnetic turbulent fluctuation spectrum is investigated in the core of a toroidally confined plasma with parameters similar to those in the fusion edge plasma. The measured spectra show fully developed turbulence over almost 6 decades down to the range of nano-Tesla field amplitudes. The magnetic fluctuations are interpreted as being due to the parallel dynamics of drift-wave turbulence. The predicted strong β dependence of the magnetic fluctuations is experimentally confirmed. For the present parameters, anomalous transport due to the magnetic turbulence can be neglected compared with the electrostatic contribution.