Apparently this is not a brand new theory http://cogweb.ucla.edu/ep/Schizovirus.html , lending credence to the idea of some sort of connection. But it would almost certainly be a prenatal connection, not due to later exposure, and would have to be at a specific stage of pregnancy. At least 30% of the US population has antibodies to the toxoplasma parasite, meaning they have been infected with it at some point, and we obviously don't have anywhere near that many schizophrenics.
However, if you read the info towards the end of the above-linked article, re toxoplasmosis in AIDS patients, another angle shows up. The effect may be due not just to the presence of the toxoplasma parasite, but to the failure of the mother's immune system to effectively ward off/limit the parasite, and this would be determined by a lot of other things that have an effect on the performance of the immune system: stress, poor nutrition, alcohol/drug abuse, etc. That would be consistent with the demographics of schizophrenia, which is more common in lower socioeconomic classes.