Last winter my rain barrel cracked in the cold - I didn't get the water out in time and winter ice ruptured the bottom. 

 

This is the kind of rain barrel I have.

 

Does anyone know how it can be repaired so I can use it again?

If it's just a hairline crack, I think it can still be repaired by bonding it with heavy duty superglue, Gorilla glue, of a Flex seal. Most of the repair work needs to be done from the inside. Clamp it well to meld the pieces together. This may only be a temporary solution until you can buy a new rainbarrel.  The repaired crack may not be able to sustain the pressure for a long time just like a new one.