Can a queen bee sting a human?

Yes, a queen bee can sting.

A worker bee has a barbed sting so can only sting once because the sting and venom sac is left in the victim when the bee pulls away. The queen has a smooth sting which she can withdraw, so she can potentially sting several times.

However, under normal circumstances you are unlikely to be stung by a queen. Soon after a new queen hatches, she goes on a mating flight where she will climb well above head height followed by the drones (male bees). After mating she returns to the hive and will not leave it again unless the colony decides to swarm to find a new home.

Within a swarm the queen would be closely guarded by the worker bees. She would not be flying free and able to sting anyone.

By the way, drones don't have a sting.