The following is an excerpt from an older article of mine discussing the link between autism and the MMR vaccine. You would be hard pressed to find a respectable authority who would suggest that a link exists between the two- this is the academic way of saying the two are not related.
Vaccines cause Autism - False. The relationship between vaccines (specifically the preservative thimerosal) and autism is based on a temporal (meaning time-relationship) argument. The MMR (Mumps-measles-rubella) vaccine is given to children at around 18 months of age (may be 16-20 months depending on the child), which is also the same time that the first clinical symptoms of autism begin to appear. This is based on one study in the UK's IBDSG department of the Royal Free Hospital in London, England done by Dr. Wakefield and colleagues with 12 children, however the relationship was only temporally linked in 8 of these children. Since then a plethora of studies have been done in the UK and US, none of which find any link between autism and vaccines. Furthermore, some studies actually report a non-relationship between vaccines and autism.
Source: Public Health Agency of Canada
I leave you with this: millions of children receive the MMR vaccine each year. Why then, do only a very small number of them develop autism? Further, there are children who develop autism who have never been vaccinated. Without biological plausibility and a dose-response relationship, Bradford Hill would have a blast with this one...