No, unless you're a law enforcement officer of some flavor, you cannot lawfully carry your handgun (or weapons) at the State Fair.
Here is the IAC (Indiana Administrative Code) for the annual Indiana State Fair (note that it is applies to all "deadly weapons," not just firearms):
“Deadly weapons prohibited
(a) This rule does not apply to a federal, state, or local law enforcement officer or to a person who has been employed or authorized by the state fair commission to provide security protection and services during the annual state fair.
(b) No person in possession of a deadly weapon shall be permitted onto or be permitted to remain on the fairgrounds during the annual state fair.
(c) Any deadly weapon found in the possession of a person while on the fairgrounds during the annual state fair is subject to immediate confiscation by law enforcement officers or other persons authorized by the executive director of the state fair commission.
(d) Any person properly licensed to carry a firearm must secure the firearm in a locked compartment of his or her vehicle, and it shall not be visible to passersby.”
80 IAC 4-4-4