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.
Statistical Yearbook of the League of Nations 1940-1941
(Mt means millions of metric tons of crude oil produced for the whole year)
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.