Cruz polled at 31 percent while real estate magnate Donald Trump — who regularly led most national polls — held a distant second place at 21 percent.
These results mirror those of Monday's Monmouth University Poll, which gave the freshman senator a five-point lead over Trump.
The top slot in Iowa has cycled among Trump, retired neurosurgeon Ben Carson and Cruz. Carson, once an evangelical voter darling, was almost an afterthought among Iowa Republican voters in comparison.
Carson polled at 13 percent, followed by Sen. Marco Rubio (R-FL) at 10 percent and former Florida Gov. Jeb Bush (R) at 6 percent.
Cruz had the support of 51 percent of likely caucusgoers when asked about their first and second choices.
Bloomberg Politics reported this 21-point jump is the largest in the Iowa polls in the last five presidential caucuses.
The last Des Moines Register/Bloomberg Politics poll of Iowa voters was conducted in late October. Carson led at 28 points, followed by Trump at 19 points and Cruz at 10 points.
The poll was conducted among 2,635 Iowans, 400 of whom were Republicans, from Dec. 7-10. The margin of error among Republican caucusgoers was plus or minus 4.9 percent.
The Iowa caucuses are February 1.