By August 15th, 1945, when Japan indicated its willingness to surrender, the US had one extra Pu-239 core ready to be shipped to Tinian for assembly into a bomb.

By the time WWII formally ended (early September 1945), they had about enough plutonium for two bomb cores, but only one (the same one as before) was fashioned into a full core, and was in "quality control" because it had been involved in a criticality accident (the Daghlian accident). Only parts of another core had been assembled (HS-7 and R-3 on this chart — "hemisphere 7," which is about half of a core, and "ring 3," which is an additional, smaller core component, and neither of those values add up to a full half-core, which is about 3 kg).

At the same time, they only had about 22 kg of high-enriched uranium (about 1/3rd of a "Little Boy" core) at Los Alamos. Their production rate of HEU was such that they probably would have had another full core by November or so (they were producing 0.6-1 kg per day at that point, and needed 64 kg for a bomb core, so that's about two months worth of additional production).

Note that the US not assemble any additional weapons at the end of WWII. So whether it had the weapons, or just the potential for weapons (the cores), is a slightly important point depending on why one wants to know the answer (e.g., they wouldn't have been able to instantly use any of these weapons).

To address another frequently asked question: the US plutonium production system created by the Manhattan Project could, at maximum production, produce three bomb cores per month, and one uranium core every two months. These are assuming they did no weapons design innovation from the bombs dropped on Hiroshima and Nagasaki. They did have some ideas on the books, that might have been pursued if the war had gone on, for making "composite" (uranium+plutonium) cores. If that had been the case then their arsenal could have been stretched out quite a bit more (it lets you use your material much more efficiently, by a factor of 3-4 or so).