Yes, you could say “I am the same way” but I wouldn’t say it would be our first choice when saying we have something in common with someone. Translated to Chinese, it would likely be “我也是那样“ or “我跟你一样“ 。Most people would probably just say “Me too” “我也是“。I hope this answers your question ~^^

Thank you, Natalia.

It evidently means "I also prefer writing letters with ...." , though for me "So do I" is a more usual way to say that.