Thanks to user:pugsville for pointing out the League of Nations reports. I chose one with a 1940 column, even though some spaces were not filled in due to war. But as it turns out, all nations producing more than a million tons of oil have a 1940 number.
http://digital.library.northwestern.edu/league/le0280ah.pdf
(Mt means millions of metric tons of crude oil produced for the whole year)
USA 182.657 Mt
USSR 29.700 Mt
Venezuela 27.443 Mt
Iran 10.426 Mt
Indonesia 7.939 Mt
Mexico 6.721 Mt
Romania 5.764 Mt
Columbia 3.636 Mt
Iraq 3.438 Mt
Argentina 2.871 Mt
Trinidad 2.844 Mt
Peru 1.776 Mt
Burma 1.088 Mt
Canada 1.082 Mt
Egypt 0.929 Mt
There are more, but I didn't bother including nations that produced less than a million metric tons of crude oil in one year (except Egypt because it was pretty close).
Interestingly, Saudi Arabia is not on the list! Apparently they had not yet found oil there. Iran and Iraq are on the list, though.