If you've already got the game installed, but want to hook it up in steam, you can either
A) click "add non steam game" and add STO to the list, which will let you use the Steam Overlay and Friends features, as well as show others when you're playing.
B) Goto the steam store, click download. Pause Download. Go to your existing STO folder, and copy it's contents to the newly made (mostly) empty steam folder, and paste it there. Once copied over, resume your steam download, which should go much more quickly. Verify the files, and you should be good to go.
P.S. I love me some Steam.
Try this. I'm not sure about B, but if it works, go for it.