When Reynolds number Re (equivalent to U(infinity)d/v, where U. is the free stream velocity, d is the cylinder diameter, and v is the kinematic viscosity of fluid) varies from 103 to 104, there is a large change in the turbulent near-wake dynamics (e.g., the base pressure coefficient, fluctuating lift coefficient, and vortex formation length) of a circular cylinder, which has previously been connected to the generation of small-scale Kelvin-Helmholtz vortices. This work aims to investigate how this Re variation affects the three components of the vorticity vector and to provide a relatively complete set of three-dimensional vorticity data. All three components of vorticity were simultaneously measured in the intermediate region of a turbulent circular-cylinder wake using a multiwire vorticity probe. It is observed that the root-mean-square values of the three vorticity components increase with Re, especially the streamwise component, which shows a large jump from Re = 5 X 10(3) to Re = 10(4). At Re = 2.5 X 10(3), the maximum phase-averaged spanwise vorticity variance (omega(z)(2))(*), normalized by d and U-infinity, is twice as large as its counterpart for the streamwise component, (omega(x)(2))(*), or the lateral component, (omega(y)(2))(*). However, at Re = 10(4), the maximum (omega(z)(2))(*) is only 55% larger than the maximum (omega(x)(2))(*) or 47% larger than the maximum (omega(y)(2))(*). The observation is consistent with the perception that the three-dimensionality of the flow is enhanced at higher Re due to the occurrence of Kelvin-Helmholtz vortices. The effect of Re on vorticity signals, spectra, and coherent and incoherent vorticity fields is also examined.