I don‘t know when exactly it became common practice in Europe, but it seems to be a very old tradition, as the user before stated, that earrings were common in the Minoan civilization already. In medeival time, it was common for both genders.

Interesting anecdote: Ever heard the German term ‚Schlitzohr‘? It translates to ‚rascal’, but the original meaning is ‚slit ear‘. It was tradition for master craftsmen and merchants to wear earrings as sign of their respectability. When they were caught cheating their customers, the earring was ripped off as a punishment. The slit ear showed that they are dishonest persons.