No, but it's close, ranking between #4 and #6 depending on how you count.
As of August 20, 2020, the US death toll from COVID-19 is roughly 175,000 (source: the New York Times, the CDC, and Worldometers all agree to within about 2%). The death toll started rising in late March, for a duration of slightly over five months, not the four months mentioned in the question.
Compare that to other death tolls (all numbers rounded to the nearest thousand):
- American Civil War, total military deaths: 593,000, including disease, over four years.
- World War II: 419,000 total, including civilian deaths, over four years.
- American Civil War, Union deaths: 335,000 total, including disease, over four years.
- 1918 flu pandemic, second wave: 292,000 over four months.
- Heart disease (#1 cause of ongoing deaths): 270,000 per five months in 2017.
- Cancer (#2 cause of ongoing deaths): 250,000 per five months in 2017.
- COVID-19 is here right now, at 175,000 deaths.
- <From here on down, only some causes of death have been listed>
- World War I: 117,000 total, including disease, over roughly a year and a half.
- Accidental injuries (#3 cause of ongoing deaths): 71,000 per five months in 2017.
- Influenza: 61,000 in the 2017-2018 flu season, the worst in the past decade.
- Vietnam War: 58,000 total, over roughly nine years.
- American Civil War, Overland Campaign: 12,000 over two months.
Sorted by percent of the population killed, using the population numbers from the nearest census. The relative rankings of some things change, but COVID-19 remains in the #6 spot
- American Civil War, total military: 1.8%
- American Civil War, Union military: 1.5%
- World War II: 0.32%
- 1918 flu pandemic, second wave: 0.28%
- Heart disease, five-month average in 2017: 0.082%
- Cancer, five-month average in 2017: 0.076%
- COVID-19, March 1-August 21: 0.054%
- <From here on down, only some causes of death have been listed>
- American Civil War, Overland Campaign: 0.038%
- Vietnam War: 0.028%
- Accidental injuries, five-month average in 2017: 0.022%
- Influenza, 2017-2018 season: 0.018%
COVID-19 isn't the biggest killer of Americans in history, but it's well up there. Compared to other disease outbreaks, it's ahead of everything except the 1918 flu pandemic. Compared to non-contagious causes of death, it's ahead of everything except heart disease and cancer. And compared to mass-casualty events such as wars, it's ahead of everything except World War II and the American Civil War -- and it's ahead of any five-month slice of either of those wars.
More people dying from COVID-19 won't change the relative ordering, barring a disastrous third wave -- the COVID-19 rate is currently lower than that for cancer or heart disease (so it won't pass them), the COVID-19 total is already ahead of the annual total for accidents (so it can't fall behind it), and the 1918 pandemic is far enough ahead of COVID-19 that it isn't likely to be surpassed, particularly as a percentage of population killed.