We apply a new method to determine the magnetic field in coronal loops, using observations of coronal loop oscillations. We analyze seven Doppler-shift oscillation events detected by SUMER in the hot flare line Fe XIX to obtain the oscillation periods of these events. The geometry, temperature, and electron density of the oscillating loops are measured from coordinated multichannel soft X-ray imaging observations from SXT. All the oscillations are consistent with standing slow waves in their fundamental mode. These parameters are used to calculate the magnetic field of coronal loops based on MHD wave theory. For the seven events, the plasma β is in the range 0.15-0.91 with a mean of 0.33 ± 0.26, and the estimated magnetic field varies between 21 and 61 G with a mean of 34 ± 14 G. With background emission subtracted, the estimated magnetic field is reduced by 9%-35%. The maximum background subtraction gives a mean of 22 ± 13 G in the range 12-51 G. We discuss measurement uncertainties and the prospect of determining coronal loop magnetic fields from future observations of coronal loops and Doppler-shift oscillations.