Is there a way to connect or transfer the profile I created and currently playing on my PC to my PS3 so in both platforms I can use the same one?
Quote from the DC Universe Website
PlayStation®3 and PlayStation®4 gamers play together on shared servers. The PC version has dedicated servers that are not shared with the PlayStation versions.
Since they both play on different servers, their data is held differently. Therefore, there is no way to transfer a data from one medium (PC) to another (PS3), unless it is between PS3 and PS4.