PC stands for Police Constable. This is a rank within the police force, and PC is the abbreviation of this title. For example, a police constable called John Smith could be referred to as PC Smith. PC Rain is a joke, referring to the fact that rainy weather suppresses crime. The job of police officers is to suppress crime, but sometimes the weather does this job for them.

In this case PC is probably an abbreviation for police constable. Since rain suppresses crime its jokingly referred to as PC Rain.

Police craft rain.