Audio file for how to say “Can I please have your autograph?” in Japanese
サインしていただけますか？ (sain shite itada kemasu ka)
In Japanese, autograph is pronounced “Sign”.
The same as when you buy something with a credit card, you need to put your “SIGN” (signature) on the dotted line.
I am guessing that’s the origin and somehow the word “sign” became to mean “autograph” in Japanese.
Since it is practically the same thing (asking for someone’s signature), I think it makes sense.