A little digging found that, depending on the brand and fat content, 1 cup of cocoa powder can weigh anywhere from 80 to 118 grams. I used Valrhona, which is on the heavy end; for comparison, I weighed 1 cup of ubiquitous Fry's, which came to 92 grams. Moral of the story: Use a scale.
Adapted from Dorie's Cookies by Dorie Greenspan.