The poll marks one of the only state-level polls outside of Iowa to show Cruz reaching Trump’s level of support.
California's presidential primary is not until June 7, the last day of contests for the GOP bid. However, thanks to a splintered field and the possibility of a brokered convention, the state's 172 delegates - the largest prize of the nomination process - could be critical for a candidate trying to reach a slim majority.
Cruz has become the front-runner in Iowa, thanks to growing support among tea party supporters and white evangelical Christians. Still, Trump leads almost all recent national polls by double digits, as well as recent polling in New Hampshire.
The Iowa caucus takes place Monday, Feb. 1.