  We study spin structures on orbifolds. In particular, we show that if the
singular set has codimension greater than 2, an orbifold is spin if and only if
its smooth part is. On compact orbifolds, we show that any non-trivial twistor
spinor admits at most one zero which is singular unless the orbifold is
conformally equivalent to a round sphere. We show the sharpness of our results
through examples.
