Gowdy drove away Sunday night and was not hurt.
Police say Gowdy had been parked in a church parking lot shortly after 8 p.m. when a woman approached his pickup truck and pointed a gun at him.
Authorities say 52-year-old Gloria Yvonne Brackett told Gowdy to stop following her. Gowdy says he tried to explain that he was not following the woman before driving away.
Brackett has been charged with pointing a gun and illegally carrying a pistol. It wasn’t known if she had an attorney.
Gowdy represents the 4th District which includes Greenville, Spartanburg, Union and part of Laurens County. The Republican was first elected in 2010.