It depends whether the transformer is connected to a power source or not.
If it isn't there will be no effect at all.
If it is, then the power source will be shorted out as well and this would cause circuit breakers or fuses to cut the power.
If it was a complete short circuit, from end to end of the primary, the transformer would be unaffected, although it would have to be repaired before it could be used.
If it was a partial short circuit, the remainder of the winding that wasn't shorted could be destroyed.
A short of just a few turns can cause overheating of the transformer.