short answer is no, you are not eligible for US citizenship just because your Grandmother is American.
Where and when was your father born? Depending on the laws at the time, he may or may not be eligible for US citizenship. However, even if he is eligible, you probably wouldn't be, because your father would have to have lived in the US for some number of years before you were born, in order to register your birth abroad as a US citizen.
Unfortately, the US does not have an Anscestry visa like the
UK does, so we are not eligible for immigration to the US based on our grandparents citizenship.