Phased array radar (PAR) holds promise for future weather surveillance technology. It has the potential to improve temporal resolution and allow significant performance and flexibility improvements compared to traditional reflector-antenna radars. Nevertheless, PARs have some drawbacks that need to be addressed. Two critical drawbacks are the variable copolar bias and cross-polar contamination. This article presents a novel technique for reducing the antenna cross-polar contamination on polarimetric measurements. The cross-polar canceller (XPC) technique is intended for fully digital phased array systems, but can also be implemented on systems with subarray-level digital signals. XPC selects canceller elements strategically throughout the array to transmit canceling signals. The canceller elements are modulated in amplitude and phase and transmit/receive in the cross-polarization to mitigate cross-polar radiation. The XPC algorithm provides the number of canceller elements, their location, and the complex coefficient per steering angle to maximize the cross-polar isolation. Calculations in this article are derived for the simultaneous transmission and simultaneous reception (STSR) mode, which simultaneously transmits electromagnetic waves in the horizontal (H) and vertical (V) polarizations. Nevertheless, they are also valid for the alternate transmission simultaneous reception (ATSR) mode. The XPC technique is being implemented in the Horus system, a fully digital, S-band, polarimetric phased array system designed by the Advanced Radar Research Center (ARRC). The analysis presented here is based on a measured Horus embedded element pattern, and a simulated $8 \times$ array. Preliminary results indicate that XPC is effective at mitigating cross-polar radiation, and significantly improving polarimetric weather measurements.