I remember when I was younger I had heard this story about the Chinese using primitive fireworks, and even strapping them to a bamboo glider in an attempt to reach the moon. This story probably isn't even true, and I shudder to think of the t/w and isp those fireworks would provide, but would it be possible to strap enough of them together to reach orbit, somewhat similarly to OTRAG, and how ridiculously large would it have to be.
Very crude back-of-the-envelope math suggests that a rocket of about one million tons -- 300 times the mass of the Saturn V -- could reach orbit on black powder from a specific impulse and mass ratio standpoint. Whether it's possible to structurally assemble a rocket of that size and launch it is questionable, at best.
In addition to Russel Borogove's answer there is also the XKCD design using modern model rocket motors and a complex staging profile that got an orbital vehicle that is 'an unstable pile of gunpowder the size of Central Park' and the British Interplanetary society black powder design that I cannot find numbers on beyond 5 stages and 'the mass of an ocean liner'. Most of the BIS design work was expended on the instrumentation and guidance of the lander rather than the launch vehicle.