My understanding is that you can get Kosher corn syrup, but that no corn product is Kosher for Passover, a stricter standard. The rules may be different for Sephardic Jews.
“In the Ashkenazi tradition there are additional foods that are usually forbidden during Passover. These foods are called “kitniot” (pronounced kit-neeh-oat) and include: rice, millet, corn and legumes like beans and lentils. These foods are off limits because the rabbis determined they violated the principle of ma’arit ayin.”
http://judaism.about.com/od/holidays/a/What-Is-Kosher-For-Passover.htm