Is there a way I can tell how old my turtle is?

If it's full-grown, no, not really, you really have no idea. If it's a baby or one to five years old, you can make an educated guess just based on the size of it, but really, their growth depends on the temperature that they're being kept in and the food that they're being offered. So an animal that has optimal conditions might be full-grown in five years, whereas an animal that maybe didn't get enough heat or food might still be very, very small in five years. There's no way to know the age of your turtle unless you know when it came out of its egg.