Is it possible to find out how long you have had Hep. C?

No, there is no method how to trace back the date or way how you were infected. There are two ways how to get some hint on this:

1st - if you have regularly done blood work (liver test), it is possible to analyze, when your ALT started to rise.
2nd - liver biopsy can answer the question, how much is your liver injured. But to connect this results with time is not possible unless you have several results from different years (what I do not expect).

Petr