not if you are in a cast. it would become so stinky that you could not stand the smell and the humidity has the potential of fostering a very itchy and irritating fungal infection. if you do not have any medical issues that would preclude you from using a sauna or steam room and you are in a boot instead of a cast hobble or hop in carefully (don't slip or fall) consider leaving the boot outside the room and enjoy. there are no reasons a person with a broken ankle cannot have a sauna or steam.
can i sit in a sauna and steam room with a broken ankle?