Helical magnetic field threading the accretion disk and the black hole likely play a key role in jet launching mechanisms in active galactic nuclei (AGNs). The flat-spectrum radio quasar (FSRQ) 1633+382 is a radio-loud AGN with well-developed jets which have been monitored with very long baseline interferometry (VLBI) over the last few decades, making an excellent target to probe the structure of magnetic fields in the parsec (pc)-scale quasar jets. From its VLBI observations over two decades, we find evidence for quasi-periodic and oscillating patterns in the positions of some jet components and their luminosities. The patterns are well explained when the jet components are assumed to be moving along helical trajectories, changing the Doppler factor and the apparent speed as the viewing angle of the jet changes. Our analysis supports the presence of a helically ordered magnetic field along the jet, which is predicted by jet theories and also suggested by previous observations.