The study analyzed health information gathered by the National Health Interview Survey (NHIS), an annual survey of American households conducted by the Centers for Disease Control and Prevention.
Between 1997 and 2016, the researchers gathered data on children between the ages of three and 17.
They found that 11.25 percent of children reportedly diagnosed with ASD have a food allergy - much more than the 4.25 percent of children not on the spectrum who have a food allergy.
The finding was observational, based purely on survey results, so Dr Bao's team could not establish whether or not an intolerance the causes autism.
But previous studies have suggested possible links including alterations in gut bacteria and increased production of antibodies and immune system overreactions.
These can lead to impaired brain function and neurodevelopmental abnormalities.
About one in every 59 children is on the autism spectrum, and the numbers seem to be growing in recent years.
But autism's root cause has continued to elude scientists, despite recent advances in studies on the disorder.
So far, the most robust explanations link autism to an imbalance in the immune system. The immune system's inflammatory response to pathogens should calm back down quickly once its job is done but, in autistic people, inflammation seems to be the predominant mode.
That discovery has led scientists to believe that autism is a function of a kind of autoimmune disorder.
Allergies, too are the result the immune system going a bit haywire, but in a way we are better at treating, leading researchers - including Dr Bao - to investigate the link between autism and respiratory-, skin- and food-related allergic reactions.
Dr Bao, whose research is published in JAMA Network Open, says these connections warrant further investigation.
He said: "We don't know which comes first, food allergy or ASD."
He added that a further study following children over many years since birth would be needed to establish this.
Earlier research on the association of allergic conditions with ASD have focused mainly on respiratory and skin allergy, such as asthma and eczema, which has been inconsistent and inconclusive.
The latest study found 18.73 percent of children with ASD suffered from respiratory allergies, while 12.08 percent of children without it had them.
Meanwhile, 16.81 percent of children with ASD had skin allergies, well above the 9.84 percent of children who are not autistic.
Dr Bao said: "This indicates there could be a shared mechanism linking different types of allergic conditions to ASD."
He concluded: 'In a nationally representative sample of US children, we found a significant and positive association of food allergy, respiratory allergy, and skin allergy with ASD.
"The association persisted after adjustment for demographic and socioeconomic variables and other types of allergic conditions.
"In addition, the association between food allergy and ASD was consistent and significant in all age, sex, and racial/ethnic subgroups.
"Further investigation is warranted to elucidate the causality and underlying mechanisms."
Almost one in 13 young children suffer from a food allergy in the US and - like autism - the intolerances are becoming increasingly common.
Autism has been suspected of being linked to allergies for more than 20 years, leading some to hope that cutting out irritants could improve autism, too.
A study two decades ago found a large proportion of autistic children, particularly those with late onset autism, responded well when fed a diet low in wheat, milk and other products linked to allergies.
But experts say diet is unlikely to be a cure, and, until the causes are better established, families can do little more than manage the symptoms.
THE SIGNS AND SYMPTOMS OF AUTISM
According to the CDC, people with autism have trouble with social, emotional and communication skills that usually develop before the age of three and last throughout a person's life.
Specific signs of autism include:
• Reactions to smell, taste, look, feel or sound are unusual
• Difficulty adapting to changes in routine
• Unable to repeat or echo what is said to them
• Difficulty expressing desires using words or motions
• Unable to discuss their own feelings or other people's
• Difficulty with acts of affection like hugging
• Prefer to be alone and avoid eye contact
• Difficulty relating to other people
• Unable to point at objects or look at objects when others point to them.
