This claim can actually be tested very easily. Others have done it, e.g. Brian Dickerson: The perils of repeating political nonsense and came to the conclusion that the claim was wrong.
You just need the chance a random person from a large group has a genius level IQ, then multiply it with the number of people in China and compare the result with the number of people in the USA. The IQ follows a Gaussian distribution where 100 is the mean by definition and a standard deviation (SD) of 15 (after Wechsler) or 16 (after Stanford-Binet). (sources: , ). The rarity of a particular IQ can be calculated easily and are listed by . This numbers give the percentage of people with an IQ equal or lower than the given IQ and the rarity of this occurring.
The main question actually is what an genius level IQ is. According to  it is 140 or higher ("Genius or near genius") while  states it as at least 160. The rarity of such an IQ is 1/261 (with a SD of 15) or 1/161 (SD=16) for an IQ of 140 and 1/31,560 (SD=15) or 1/11,307 (SD=16) for an IQ of 160 .
The population of USA for 2012 is about 313,221,000 according to the U.S. Census Bureau . The population of China for 2011 is about 1,370,537,000 . Taking the lowest rarity of 1/161 from above then there are about 1,370,537,000/161 = about 8,513,000 geniuses in China, which is significant less then the 313,221,000 Americans. If you take the 15 SD value of 1/261 then you get only about 5,251,000 Chinese geniuses. With the 160 IQ points, which are more realistic  to indicate a real genius, the numbers are even much less (about 43,400 or 12,100). Note that 1,370,537,000/313,221,000 = 4.375, so in order for this claim to be true actually one of every four (or say five) Chinese would need to be a Genius. Even without the numbers above, it can be easily understood that this is not the case.
*The above calculation is based on the assumption that China has a mean IQ of 100. Various studies had shown that China and other East Asian countries have a mean IQ of around half a standard deviation above the mean (one source claims 106, others have claimed as high as 115) 8
What this means is that the normal curve for China is shifted to the right of the world's normal curve, and if we assume the same standard deviation for China, then about 2 SD would be enough to reach 140 IQ, 2 SD is 95%. So roughly 1/20 people in China have 140 IQ or above. This number still doesn't reach the entire population of USA, but it comes a lot closer.
Conclusion: This claim is wrong according to the definition and probabilities of the IQ.