We have analyzed the total intensity, spectral index, linear polarization, and rotation measure (RM) distributions at the parsec scale for the quasar 1604+159. The source was observed at 5.0, 8.4, and 15.4 GHz in 2002 and 4.6, 5.1, 6.0, 7.8, 12.2, 15.2, and 43.9 GHz in 2020 with the American Very Long Baseline Array (VLBA). Combining the polarization results of Monitoring of Jets in Active Galactic Nuclei with VLBA Experiments at 15 GHz from 2009 to 2013, we studied the evolution of magnetic field at the parsec scale for the source. We detected a core-jet structure. The jet extends to the distance of ∼25 mas from the core at a direction of ∼66° north by east. The shape of the jet derived from 15 GHz data varies slightly with time and could be described by a straight line. Based on the linear polarization distribution in 2002, we divided the source structure into the central region and the jet region. In the jet region, we find the polarized emission varies with time. The flatter spectral index values and electric vector position angle direction indicate the possible existence of shocks, contributing to the variation of polarization in the jet with time. In the central region, the derived core shift index k r values indicate that the core in 2002 is close to the equipartition case, while it deviated from the case in 2020. The measured magnetic field strength in 2020 is 2 orders of magnitude lower than that in 2002. We detected transverse RM gradients, evidence of a helical magnetic field, in the core. The polarized emission orients in general toward the jet direction in the core. At 15 GHz, in the place close to the jet base, the polarization direction changes significantly with time from perpendicular to parallel to the jet direction. The evolution of RM and magnetic field structure are potential reasons for the observed polarization change. The core ∣RM∣ in 2020 increases with frequency following a power law with index a = 2.7 ± 0.5, suggesting a fast electron density falloff in the medium with distance from the jet base.