Census Bureau’s Supplemental Poverty Measure
Nah, according to that metric they have a supplemental poverty rate of 23.8% compared to the overall SPM of the US of 16%. So California has about 1.5x the national average (for this particular version of the poverty rate) and 12% of the population of the US. Therefore, they would have 18% of the country's "poor" or less than 1/5.
Unless you have different numbers or different math.
Going more explicitly: California has a population of 39.8m and 23.8% of those are within the SPM designation or 9.401m. USA has a population of 327.2m and 16% of those are within SPM or 52.35m. That means California has 9.401/52.35*100% or 18% of the "poor".
Works out the same but I felt like checking my original guesstimate math.