  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
oscillation periods of these events. The geometry, temperature, and electron
density of the oscillating loops are measured from coordinated multi-channel
soft X-ray imaging observations from SXT. All the oscillations are consistent
with standing slow waves in their fundamental mode. The parameters are used to
calculate the magnetic field of coronal loops based on MHD wave theory. For the
seven events, the plasma $\beta$ is in the range 0.15-0.91 with a mean of
0.33$\pm$0.26, and the estimated magnetic field varies between 21-61 G with a
mean of 34$\pm$14 G. With background emission subtracted, the estimated
magnetic field is reduced by 9%-35%. The maximum backgroud subtraction gives a
mean of 22$\pm$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.
