Possible- it would be more of a surprise if alternate history wasn't composed of alternate people after all- but start at the end and work backwards; under what circumstances would America be willing to elect George S. Patton? What is the problem to which he would look like the solution?
Assuming that he is actually alive to elect, that necessarily- a major cold war confrontation early on, perhaps, might make him look good.
Say McArthur drops the ball spectacularly during the Korean War; or Stalin suffers a severe attack of lizard- brain, and the hordes pouring south over the border are not Chinese, they're the Soviet Far Eastern Strategic Direction.
A catastrophic conventional defeat, fast enough to amount to a fait accompli before the orders can be passed along the nuclear chain of command; America's Viceroy of Japan dead, the entire eighth (US) army dead or prisoner, Korea in Soviet hands, revenge for the humiliation of the Berlin Airlift.
In conditions like that, Patton might have a shot at the 1952 elections. America might actually want someone like him, in a much hotter cold war.
Probably still well into fever dream territory, though.