We present polarization measurements at 8.4, 22, and 43 GHz made with the VLA of a complete sample of extragalactic sources stronger than 1 Jy in the 5-year WMAP catalogue and with declinations north of -34 degrees. The observations were motivated by the need to know the polarization properties of radio sources at frequencies of tens of GHz in order to subtract polarized foregrounds for future sensitive Cosmic Microwave Background (CMB) experiments. The total intensity and polarization measurements are generally consistent with comparable VLA calibration measurements for less-variable sources, and within a similar range to WMAP fluxes for unresolved sources. A further paper will present correlations between measured parameters and derive implications for CMB measurements.