Can I become a Police Special Constable if I have been arrested before?

No you can't. Anything that would bring the administration of justice into disrepute or anything that would cast aspersions on the service would be thoroughly looked at during your background investigation. Lesser things than a "wrongful" arrest have kept better people than you out of law enforcement. And quite frankly, I don't wanna work with anyone that has that kind of history...it makes us all look bad. Just stick to your lawyer career...