Board of Equalization member Betty Yee is the pick for 19 percent of likely voters.
Assembly Speaker John Perez comes in third with 14 percent.
Another 1 percent prefer other candidates, and 38 percent are undecided.
The Field Poll says Swearengin's lead is largely because of her strong backing by fellow Republicans. On the other hand, Democrats Yee and Perez are splitting the support of their party.
The two leading candidates in the June primary will face off in the general election this fall.